Pre-Algebra Examples

$- 3 (x + 4) + 4 (x - 3) (x - 2) = 3 (x + 1)$

Step 1

Simplify $- 3 (x + 4) + 4 (x - 3) (x - 2)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$- 3 x - 3 \cdot 4 + 4 (x - 3) (x - 2) = 3 (x + 1)$

Step 1.1.2

Multiply $- 3$ by $4$ .

$- 3 x - 12 + 4 (x - 3) (x - 2) = 3 (x + 1)$

Step 1.1.3

Apply the distributive property.

$- 3 x - 12 + (4 x + 4 \cdot - 3) (x - 2) = 3 (x + 1)$

Step 1.1.4

Multiply $4$ by $- 3$ .

$- 3 x - 12 + (4 x - 12) (x - 2) = 3 (x + 1)$

Step 1.1.5

Expand $(4 x - 12) (x - 2)$ using the FOIL Method.

Tap for more steps...

Step 1.1.5.1

Apply the distributive property.

$- 3 x - 12 + 4 x (x - 2) - 12 (x - 2) = 3 (x + 1)$

Step 1.1.5.2

Apply the distributive property.

$- 3 x - 12 + 4 x \cdot x + 4 x \cdot - 2 - 12 (x - 2) = 3 (x + 1)$

Step 1.1.5.3

Apply the distributive property.

$- 3 x - 12 + 4 x \cdot x + 4 x \cdot - 2 - 12 x - 12 \cdot - 2 = 3 (x + 1)$

Step 1.1.6

Simplify and combine like terms.

Tap for more steps...

Step 1.1.6.1

Simplify each term.

Tap for more steps...

Step 1.1.6.1.1

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1.6.1.1.1

Move $x$ .

$- 3 x - 12 + 4 (x \cdot x) + 4 x \cdot - 2 - 12 x - 12 \cdot - 2 = 3 (x + 1)$

Step 1.1.6.1.1.2

Multiply $x$ by $x$ .

$- 3 x - 12 + 4 x^{2} + 4 x \cdot - 2 - 12 x - 12 \cdot - 2 = 3 (x + 1)$

Step 1.1.6.1.2

Multiply $- 2$ by $4$ .

$- 3 x - 12 + 4 x^{2} - 8 x - 12 x - 12 \cdot - 2 = 3 (x + 1)$

Step 1.1.6.1.3

Multiply $- 12$ by $- 2$ .

$- 3 x - 12 + 4 x^{2} - 8 x - 12 x + 24 = 3 (x + 1)$

Step 1.1.6.2

Subtract $12 x$ from $- 8 x$ .

$- 3 x - 12 + 4 x^{2} - 20 x + 24 = 3 (x + 1)$

Step 1.2

Simplify by adding terms.

Tap for more steps...

Step 1.2.1

Subtract $20 x$ from $- 3 x$ .

$- 23 x - 12 + 4 x^{2} + 24 = 3 (x + 1)$

Step 1.2.2

Add $- 12$ and $24$ .

$- 23 x + 4 x^{2} + 12 = 3 (x + 1)$

Step 2

Simplify $3 (x + 1)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$- 23 x + 4 x^{2} + 12 = 3 x + 3 \cdot 1$

Step 2.2

Multiply $3$ by $1$ .

$- 23 x + 4 x^{2} + 12 = 3 x + 3$

Step 3

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $3 x$ from both sides of the equation.

$- 23 x + 4 x^{2} + 12 - 3 x = 3$

Step 3.2

Subtract $3 x$ from $- 23 x$ .

$- 26 x + 4 x^{2} + 12 = 3$

Step 4

Move all terms to the left side of the equation and simplify.

Tap for more steps...

Step 4.1

Subtract $3$ from both sides of the equation.

$- 26 x + 4 x^{2} + 12 - 3 = 0$

Step 4.2

Subtract $3$ from $12$ .

$- 26 x + 4 x^{2} + 9 = 0$

Step 5

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 6

Substitute the values $a = 4$ , $b = - 26$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{26 \pm \sqrt{{(- 26)}^{2} - 4 \cdot (4 \cdot 9)}}{2 \cdot 4}$

Step 7

Simplify.

Tap for more steps...

Step 7.1

Simplify the numerator.

Tap for more steps...

Step 7.1.1

Raise $- 26$ to the power of $2$ .

$x = \frac{26 \pm \sqrt{676 - 4 \cdot 4 \cdot 9}}{2 \cdot 4}$

Step 7.1.2

Multiply $- 4 \cdot 4 \cdot 9$ .

Tap for more steps...

Step 7.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{26 \pm \sqrt{676 - 16 \cdot 9}}{2 \cdot 4}$

Step 7.1.2.2

Multiply $- 16$ by $9$ .

$x = \frac{26 \pm \sqrt{676 - 144}}{2 \cdot 4}$

Step 7.1.3

Subtract $144$ from $676$ .

$x = \frac{26 \pm \sqrt{532}}{2 \cdot 4}$

Step 7.1.4

Rewrite $532$ as $2^{2} \cdot 133$ .

Tap for more steps...

Step 7.1.4.1

Factor $4$ out of $532$ .

$x = \frac{26 \pm \sqrt{4 (133)}}{2 \cdot 4}$

Step 7.1.4.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{26 \pm \sqrt{2^{2} \cdot 133}}{2 \cdot 4}$

Step 7.1.5

Pull terms out from under the radical.

$x = \frac{26 \pm 2 \sqrt{133}}{2 \cdot 4}$

Step 7.2

Multiply $2$ by $4$ .

$x = \frac{26 \pm 2 \sqrt{133}}{8}$

Step 7.3

Simplify $\frac{26 \pm 2 \sqrt{133}}{8}$ .

$x = \frac{13 \pm \sqrt{133}}{4}$

Step 8

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

Raise $- 26$ to the power of $2$ .

$x = \frac{26 \pm \sqrt{676 - 4 \cdot 4 \cdot 9}}{2 \cdot 4}$

Step 8.1.2

Multiply $- 4 \cdot 4 \cdot 9$ .

Tap for more steps...

Step 8.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{26 \pm \sqrt{676 - 16 \cdot 9}}{2 \cdot 4}$

Step 8.1.2.2

Multiply $- 16$ by $9$ .

$x = \frac{26 \pm \sqrt{676 - 144}}{2 \cdot 4}$

Step 8.1.3

Subtract $144$ from $676$ .

$x = \frac{26 \pm \sqrt{532}}{2 \cdot 4}$

Step 8.1.4

Rewrite $532$ as $2^{2} \cdot 133$ .

Tap for more steps...

Step 8.1.4.1

Factor $4$ out of $532$ .

$x = \frac{26 \pm \sqrt{4 (133)}}{2 \cdot 4}$

Step 8.1.4.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{26 \pm \sqrt{2^{2} \cdot 133}}{2 \cdot 4}$

Step 8.1.5

Pull terms out from under the radical.

$x = \frac{26 \pm 2 \sqrt{133}}{2 \cdot 4}$

Step 8.2

Multiply $2$ by $4$ .

$x = \frac{26 \pm 2 \sqrt{133}}{8}$

Step 8.3

Simplify $\frac{26 \pm 2 \sqrt{133}}{8}$ .

$x = \frac{13 \pm \sqrt{133}}{4}$

Step 8.4

Change the $\pm$ to $+$ .

$x = \frac{13 + \sqrt{133}}{4}$

Step 9

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Tap for more steps...

Step 9.1

Simplify the numerator.

Tap for more steps...

Step 9.1.1

Raise $- 26$ to the power of $2$ .

$x = \frac{26 \pm \sqrt{676 - 4 \cdot 4 \cdot 9}}{2 \cdot 4}$

Step 9.1.2

Multiply $- 4 \cdot 4 \cdot 9$ .

Tap for more steps...

Step 9.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{26 \pm \sqrt{676 - 16 \cdot 9}}{2 \cdot 4}$

Step 9.1.2.2

Multiply $- 16$ by $9$ .

$x = \frac{26 \pm \sqrt{676 - 144}}{2 \cdot 4}$

Step 9.1.3

Subtract $144$ from $676$ .

$x = \frac{26 \pm \sqrt{532}}{2 \cdot 4}$

Step 9.1.4

Rewrite $532$ as $2^{2} \cdot 133$ .

Tap for more steps...

Step 9.1.4.1

Factor $4$ out of $532$ .

$x = \frac{26 \pm \sqrt{4 (133)}}{2 \cdot 4}$

Step 9.1.4.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{26 \pm \sqrt{2^{2} \cdot 133}}{2 \cdot 4}$

Step 9.1.5

Pull terms out from under the radical.

$x = \frac{26 \pm 2 \sqrt{133}}{2 \cdot 4}$

Step 9.2

Multiply $2$ by $4$ .

$x = \frac{26 \pm 2 \sqrt{133}}{8}$

Step 9.3

Simplify $\frac{26 \pm 2 \sqrt{133}}{8}$ .

$x = \frac{13 \pm \sqrt{133}}{4}$

Step 9.4

Change the $\pm$ to $-$ .

$x = \frac{13 - \sqrt{133}}{4}$

Step 10

The final answer is the combination of both solutions.

$x = \frac{13 + \sqrt{133}}{4}, \frac{13 - \sqrt{133}}{4}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13 + \sqrt{133}}{4}, \frac{13 - \sqrt{133}}{4}$

Decimal Form:

$x = 6.13314064 \dots, 0.36685935 \dots$