Pre-Algebra Examples

$(x + 6) (5 x + 2) = - 23$

Step 1

Simplify $(x + 6) (5 x + 2)$ .

Tap for more steps...

Step 1.1

Expand $(x + 6) (5 x + 2)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$x (5 x + 2) + 6 (5 x + 2) = - 23$

Step 1.1.2

Apply the distributive property.

$x (5 x) + x \cdot 2 + 6 (5 x + 2) = - 23$

Step 1.1.3

Apply the distributive property.

$x (5 x) + x \cdot 2 + 6 (5 x) + 6 \cdot 2 = - 23$

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.

$5 x \cdot x + x \cdot 2 + 6 (5 x) + 6 \cdot 2 = - 23$

Step 1.2.1.2

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

Tap for more steps...

Step 1.2.1.2.1

Move $x$ .

$5 (x \cdot x) + x \cdot 2 + 6 (5 x) + 6 \cdot 2 = - 23$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$5 x^{2} + x \cdot 2 + 6 (5 x) + 6 \cdot 2 = - 23$

Step 1.2.1.3

Move $2$ to the left of $x$ .

$5 x^{2} + 2 \cdot x + 6 (5 x) + 6 \cdot 2 = - 23$

Step 1.2.1.4

Multiply $5$ by $6$ .

$5 x^{2} + 2 x + 30 x + 6 \cdot 2 = - 23$

Step 1.2.1.5

Multiply $6$ by $2$ .

$5 x^{2} + 2 x + 30 x + 12 = - 23$

Step 1.2.2

Add $2 x$ and $30 x$ .

$5 x^{2} + 32 x + 12 = - 23$

Step 2

Add $23$ to both sides of the equation.

$5 x^{2} + 32 x + 12 + 23 = 0$

Step 3

Add $12$ and $23$ .

$5 x^{2} + 32 x + 35 = 0$

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 $a \cdot c = 5 \cdot 35 = 175$ and whose sum is $b = 32$ .

Tap for more steps...

Step 4.1.1

Factor $32$ out of $32 x$ .

$5 x^{2} + 32 (x) + 35 = 0$

Step 4.1.2

Rewrite $32$ as $7$ plus $25$

$5 x^{2} + (7 + 25) x + 35 = 0$

Step 4.1.3

Apply the distributive property.

$5 x^{2} + 7 x + 25 x + 35 = 0$

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.

$(5 x^{2} + 7 x) + 25 x + 35 = 0$

Step 4.2.2

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

$x (5 x + 7) + 5 (5 x + 7) = 0$

Step 4.3

Factor the polynomial by factoring out the greatest common factor, $5 x + 7$ .

$(5 x + 7) (x + 5) = 0$

Step 5

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

$5 x + 7 = 0$

$x + 5 = 0$

Step 6

Set $5 x + 7$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 6.1

Set $5 x + 7$ equal to $0$ .

$5 x + 7 = 0$

Step 6.2

Solve $5 x + 7 = 0$ for $x$ .

Tap for more steps...

Step 6.2.1

Subtract $7$ from both sides of the equation.

$5 x = - 7$

Step 6.2.2

Divide each term in $5 x = - 7$ by $5$ and simplify.

Tap for more steps...

Step 6.2.2.1

Divide each term in $5 x = - 7$ by $5$ .

$\frac{5 x}{5} = \frac{- 7}{5}$

Step 6.2.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 7}{5}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{5}$

Step 6.2.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{7}{5}$

Step 7

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

Tap for more steps...

Step 7.1

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

$x + 5 = 0$

Step 7.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 8

The final solution is all the values that make $(5 x + 7) (x + 5) = 0$ true.

$x = - \frac{7}{5}, - 5$