Solve by Factoring 4x^2+9x-63=0

$4 x^{2} + 9 x - 63 = 0$

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 $a \cdot c = 4 \cdot - 63 = - 252$ and whose sum is $b = 9$ .

Factor $9$ out of $9 x$ .

$4 x^{2} + 9 (x) - 63 = 0$

Rewrite $9$ as $- 12$ plus $21$

$4 x^{2} + (- 12 + 21) x - 63 = 0$

Apply the distributive property.

$4 x^{2} - 12 x + 21 x - 63 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 12 x) + 21 x - 63 = 0$

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

$4 x (x - 3) + 21 (x - 3) = 0$

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

$(x - 3) (4 x + 21) = 0$

Step 2

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

$x - 3 = 0$

$4 x + 21 = 0$

Step 3

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 4

Set $4 x + 21$ equal to $0$ and solve for $x$ .

Set $4 x + 21$ equal to $0$ .

$4 x + 21 = 0$

Solve $4 x + 21 = 0$ for $x$ .

Subtract $21$ from both sides of the equation.

$4 x = - 21$

Divide each term in $4 x = - 21$ by $4$ and simplify.

Divide each term in $4 x = - 21$ by $4$ .

$\frac{4 x}{4} = \frac{- 21}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 21}{4}$

Divide $x$ by $1$ .

$x = \frac{- 21}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{21}{4}$

Step 5

The final solution is all the values that make $(x - 3) (4 x + 21) = 0$ true.

$x = 3, - \frac{21}{4}$

Solve by Factoring 4x^2+9x-63=0

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