Solve by Factoring 9x^2+21x-8=0

$9 x^{2} + 21 x - 8 = 0$

Step 1

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 $a \cdot c = 9 \cdot - 8 = - 72$ and whose sum is $b = 21$ .

Factor $21$ out of $21 x$ .

$9 x^{2} + 21 (x) - 8 = 0$

Rewrite $21$ as $- 3$ plus $24$

$9 x^{2} + (- 3 + 24) x - 8 = 0$

Apply the distributive property.

$9 x^{2} - 3 x + 24 x - 8 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{2} - 3 x) + 24 x - 8 = 0$

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

$3 x (3 x - 1) + 8 (3 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$(3 x - 1) (3 x + 8) = 0$

Step 2

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

$3 x - 1 = 0$

$3 x + 8 = 0$

Step 3

Set $3 x - 1$ equal to $0$ and solve for $x$ .

Set $3 x - 1$ equal to $0$ .

$3 x - 1 = 0$

Solve $3 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$3 x = 1$

Divide each term in $3 x = 1$ by $3$ and simplify.

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3}$

Step 4

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

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

$3 x + 8 = 0$

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

Subtract $8$ from both sides of the equation.

$3 x = - 8$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

The final solution is all the values that make $(3 x - 1) (3 x + 8) = 0$ true.

$x = \frac{1}{3}, - \frac{8}{3}$

Solve by Factoring 9x^2+21x-8=0

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