Solve by Factoring 15x^2-16+8x=0

$15 x^{2} - 16 + 8 x = 0$

Step 1

Factor by grouping.

Reorder terms.

$15 x^{2} + 8 x - 16 = 0$

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 $a \cdot c = 15 \cdot - 16 = - 240$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$15 x^{2} + 8 (x) - 16 = 0$

Rewrite $8$ as $- 12$ plus $20$

$15 x^{2} + (- 12 + 20) x - 16 = 0$

Apply the distributive property.

$15 x^{2} - 12 x + 20 x - 16 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} - 12 x) + 20 x - 16 = 0$

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

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

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

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

Step 2

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

$5 x - 4 = 0$

$3 x + 4 = 0$

Step 3

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 $x$ .

Add $4$ to 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 $1$ .

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

Step 4

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

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

$3 x + 4 = 0$

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

Subtract $4$ from both sides of the equation.

$3 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

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

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

Solve by Factoring 15x^2-16+8x=0

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