Pre-Algebra Examples

$(x + 3) \cdot (2 x - 1) = 9$

Step 1

Simplify $(x + 3) \cdot (2 x - 1)$ .

Tap for more steps...

Step 1.1

Expand $(x + 3) (2 x - 1)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$x (2 x - 1) + 3 (2 x - 1) = 9$

Step 1.1.2

Apply the distributive property.

$x (2 x) + x \cdot - 1 + 3 (2 x - 1) = 9$

Step 1.1.3

Apply the distributive property.

$x (2 x) + x \cdot - 1 + 3 (2 x) + 3 \cdot - 1 = 9$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 1 + 3 (2 x) + 3 \cdot - 1 = 9$

Step 1.2.1.2

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

Tap for more steps...

Step 1.2.1.2.1

Move $x$ .

$2 (x \cdot x) + x \cdot - 1 + 3 (2 x) + 3 \cdot - 1 = 9$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + x \cdot - 1 + 3 (2 x) + 3 \cdot - 1 = 9$

Step 1.2.1.3

Move $- 1$ to the left of $x$ .

$2 x^{2} - 1 \cdot x + 3 (2 x) + 3 \cdot - 1 = 9$

Step 1.2.1.4

Rewrite $- 1 x$ as $- x$ .

$2 x^{2} - x + 3 (2 x) + 3 \cdot - 1 = 9$

Step 1.2.1.5

Multiply $2$ by $3$ .

$2 x^{2} - x + 6 x + 3 \cdot - 1 = 9$

Step 1.2.1.6

Multiply $3$ by $- 1$ .

$2 x^{2} - x + 6 x - 3 = 9$

Step 1.2.2

Add $- x$ and $6 x$ .

$2 x^{2} + 5 x - 3 = 9$

Step 2

Subtract $9$ from both sides of the equation.

$2 x^{2} + 5 x - 3 - 9 = 0$

Step 3

Subtract $9$ from $- 3$ .

$2 x^{2} + 5 x - 12 = 0$

Step 4

Factor by grouping.

Tap for more steps...

Step 4.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 12 = - 24$ and whose sum is $b = 5$ .

Tap for more steps...

Step 4.1.1

Factor $5$ out of $5 x$ .

$2 x^{2} + 5 (x) - 12 = 0$

Step 4.1.2

Rewrite $5$ as $- 3$ plus $8$

$2 x^{2} + (- 3 + 8) x - 12 = 0$

Step 4.1.3

Apply the distributive property.

$2 x^{2} - 3 x + 8 x - 12 = 0$

Step 4.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 4.2.1

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x) + 8 x - 12 = 0$

Step 4.2.2

Factor out the greatest common factor (GCF) from each group.

$x (2 x - 3) + 4 (2 x - 3) = 0$

Step 4.3

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (x + 4) = 0$

Step 5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 3 = 0$

$x + 4 = 0$

Step 6

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 6.1

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Step 6.2

Solve $2 x - 3 = 0$ for $x$ .

Tap for more steps...

Step 6.2.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 6.2.2

Divide each term in $2 x = 3$ by $2$ and simplify.

Tap for more steps...

Step 6.2.2.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 6.2.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 7

Set $x + 4$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 7.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Step 7.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 8

The final solution is all the values that make $(2 x - 3) (x + 4) = 0$ true.

$x = \frac{3}{2}, - 4$