Solve by Factoring 15=8x^2-14x

$15 = 8 x^{2} - 14 x$

Step 1

Move all the expressions to the left side of the equation.

Subtract $8 x^{2}$ from both sides of the equation.

$15 - 8 x^{2} = - 14 x$

Add $14 x$ to both sides of the equation.

$15 - 8 x^{2} + 14 x = 0$

Step 2

Factor by grouping.

Reorder terms.

$- 8 x^{2} + 14 x + 15 = 0$

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 $a \cdot c = - 8 \cdot 15 = - 120$ and whose sum is $b = 14$ .

Factor $14$ out of $14 x$ .

$- 8 x^{2} + 14 (x) + 15 = 0$

Rewrite $14$ as $- 6$ plus $20$

$- 8 x^{2} + (- 6 + 20) x + 15 = 0$

Apply the distributive property.

$- 8 x^{2} - 6 x + 20 x + 15 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- 8 x^{2} - 6 x) + 20 x + 15 = 0$

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

$2 x (- 4 x - 3) - 5 (- 4 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $- 4 x - 3$ .

$(- 4 x - 3) (2 x - 5) = 0$

Step 3

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

$- 4 x - 3 = 0$

$2 x - 5 = 0$

Step 4

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

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

$- 4 x - 3 = 0$

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

Add $3$ to both sides of the equation.

$- 4 x = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

Set $2 x - 5$ equal to $0$ and solve for $x$ .

Set $2 x - 5$ equal to $0$ .

$2 x - 5 = 0$

Solve $2 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Step 6

The final solution is all the values that make $(- 4 x - 3) (2 x - 5) = 0$ true.

$x = - \frac{3}{4}, \frac{5}{2}$

Solve by Factoring 15=8x^2-14x

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