Solve by Factoring 8x^2+21=-59x

$8 x^{2} + 21 = - 59 x$

Step 1

Add $59 x$ to both sides of the equation.

$8 x^{2} + 21 + 59 x = 0$

Step 2

Factor by grouping.

Reorder terms.

$8 x^{2} + 59 x + 21 = 0$

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 $a \cdot c = 8 \cdot 21 = 168$ and whose sum is $b = 59$ .

Factor $59$ out of $59 x$ .

$8 x^{2} + 59 (x) + 21 = 0$

Rewrite $59$ as $3$ plus $56$

$8 x^{2} + (3 + 56) x + 21 = 0$

Apply the distributive property.

$8 x^{2} + 3 x + 56 x + 21 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} + 3 x) + 56 x + 21 = 0$

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

$x (8 x + 3) + 7 (8 x + 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $8 x + 3$ .

$(8 x + 3) (x + 7) = 0$

Step 3

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

$8 x + 3 = 0$

$x + 7 = 0$

Step 4

Set $8 x + 3$ equal to $0$ and solve for $x$ .

Set $8 x + 3$ equal to $0$ .

$8 x + 3 = 0$

Solve $8 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$8 x = - 3$

Divide each term in $8 x = - 3$ by $8$ and simplify.

Divide each term in $8 x = - 3$ by $8$ .

$\frac{8 x}{8} = \frac{- 3}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 3}{8}$

Divide $x$ by $1$ .

$x = \frac{- 3}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{8}$

Step 5

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

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

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 6

The final solution is all the values that make $(8 x + 3) (x + 7) = 0$ true.

$x = - \frac{3}{8}, - 7$

Solve by Factoring 8x^2+21=-59x

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