Solve by Factoring 5x^2-36x=32

$5 x^{2} - 36 x = 32$

Step 1

Subtract $32$ from both sides of the equation.

$5 x^{2} - 36 x - 32 = 0$

Step 2

Factor by grouping.

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 $a \cdot c = 5 \cdot - 32 = - 160$ and whose sum is $b = - 36$ .

Factor $- 36$ out of $- 36 x$ .

$5 x^{2} - 36 x - 32 = 0$

Rewrite $- 36$ as $4$ plus $- 40$

$5 x^{2} + (4 - 40) x - 32 = 0$

Apply the distributive property.

$5 x^{2} + 4 x - 40 x - 32 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 4 x) - 40 x - 32 = 0$

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

$x (5 x + 4) - 8 (5 x + 4) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x + 4$ .

$(5 x + 4) (x - 8) = 0$

Step 3

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

$5 x + 4 = 0$

$x - 8 = 0$

Step 4

Set $5 x + 4$ equal to $0$ and solve for $x$ .

Set $5 x + 4$ equal to $0$ .

$5 x + 4 = 0$

Solve $5 x + 4 = 0$ for $x$ .

Subtract $4$ from both sides of the equation.

$5 x = - 4$

Divide each term in $5 x = - 4$ by $5$ and simplify.

Divide each term in $5 x = - 4$ by $5$ .

$\frac{5 x}{5} = \frac{- 4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 4}{5}$

Divide $x$ by $1$ .

$x = \frac{- 4}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{4}{5}$

Step 5

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Step 6

The final solution is all the values that make $(5 x + 4) (x - 8) = 0$ true.

$x = - \frac{4}{5}, 8$

Solve by Factoring 5x^2-36x=32

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