Algebra Examples

$2 x (10 x + 8) = - 3 (x + 1)$

Step 1

Simplify $2 x (10 x + 8)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + 2 x (10 x + 8) = - 3 (x + 1)$

Step 1.2

Simplify by multiplying through.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$2 x (10 x) + 2 x \cdot 8 = - 3 (x + 1)$

Step 1.2.2

Simplify the expression.

Tap for more steps...

Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 10 x \cdot x + 2 x \cdot 8 = - 3 (x + 1)$

Step 1.2.2.2

Multiply $8$ by $2$ .

$2 \cdot 10 x \cdot x + 16 x = - 3 (x + 1)$

Step 1.3

Simplify each term.

Tap for more steps...

Step 1.3.1

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

Tap for more steps...

Step 1.3.1.1

Move $x$ .

$2 \cdot 10 (x \cdot x) + 16 x = - 3 (x + 1)$

Step 1.3.1.2

Multiply $x$ by $x$ .

$2 \cdot 10 x^{2} + 16 x = - 3 (x + 1)$

Step 1.3.2

Multiply $2$ by $10$ .

$20 x^{2} + 16 x = - 3 (x + 1)$

Step 2

Simplify $- 3 (x + 1)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$20 x^{2} + 16 x = - 3 x - 3 \cdot 1$

Step 2.2

Multiply $- 3$ by $1$ .

$20 x^{2} + 16 x = - 3 x - 3$

Step 3

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

Tap for more steps...

Step 3.1

Add $3 x$ to both sides of the equation.

$20 x^{2} + 16 x + 3 x = - 3$

Step 3.2

Add $16 x$ and $3 x$ .

$20 x^{2} + 19 x = - 3$

Step 4

Add $3$ to both sides of the equation.

$20 x^{2} + 19 x + 3 = 0$

Step 5

Factor by grouping.

Tap for more steps...

Step 5.1

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 $a \cdot c = 20 \cdot 3 = 60$ and whose sum is $b = 19$ .

Tap for more steps...

Step 5.1.1

Factor $19$ out of $19 x$ .

$20 x^{2} + 19 (x) + 3 = 0$

Step 5.1.2

Rewrite $19$ as $4$ plus $15$

$20 x^{2} + (4 + 15) x + 3 = 0$

Step 5.1.3

Apply the distributive property.

$20 x^{2} + 4 x + 15 x + 3 = 0$

Step 5.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 5.2.1

Group the first two terms and the last two terms.

$(20 x^{2} + 4 x) + 15 x + 3 = 0$

Step 5.2.2

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

$4 x (5 x + 1) + 3 (5 x + 1) = 0$

Step 5.3

Factor the polynomial by factoring out the greatest common factor, $5 x + 1$ .

$(5 x + 1) (4 x + 3) = 0$

Step 6

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

$5 x + 1 = 0$

$4 x + 3 = 0$

Step 7

Set $5 x + 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 7.1

Set $5 x + 1$ equal to $0$ .

$5 x + 1 = 0$

Step 7.2

Solve $5 x + 1 = 0$ for $x$ .

Tap for more steps...

Step 7.2.1

Subtract $1$ from both sides of the equation.

$5 x = - 1$

Step 7.2.2

Divide each term in $5 x = - 1$ by $5$ and simplify.

Tap for more steps...

Step 7.2.2.1

Divide each term in $5 x = - 1$ by $5$ .

$\frac{5 x}{5} = \frac{- 1}{5}$

Step 7.2.2.2

Simplify the left side.

Tap for more steps...

Step 7.2.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 7.2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 1}{5}$

Step 7.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{5}$

Step 7.2.2.3

Simplify the right side.

Tap for more steps...

Step 7.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Step 8

Set $4 x + 3$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 8.1

Set $4 x + 3$ equal to $0$ .

$4 x + 3 = 0$

Step 8.2

Solve $4 x + 3 = 0$ for $x$ .

Tap for more steps...

Step 8.2.1

Subtract $3$ from both sides of the equation.

$4 x = - 3$

Step 8.2.2

Divide each term in $4 x = - 3$ by $4$ and simplify.

Tap for more steps...

Step 8.2.2.1

Divide each term in $4 x = - 3$ by $4$ .

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

Step 8.2.2.2

Simplify the left side.

Tap for more steps...

Step 8.2.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 8.2.2.2.1.1

Cancel the common factor.

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

Step 8.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 8.2.2.3

Simplify the right side.

Tap for more steps...

Step 8.2.2.3.1

Move the negative in front of the fraction.

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

Step 9

The final solution is all the values that make $(5 x + 1) (4 x + 3) = 0$ true.

$x = - \frac{1}{5}, - \frac{3}{4}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{5}, - \frac{3}{4}$

Decimal Form:

$x = - 0.2, - 0.75$