Solve by Factoring 4x^2-4x-24=0

$4 x^{2} - 4 x - 24 = 0$

Step 1

Factor $4$ out of $4 x^{2} - 4 x - 24$ .

Factor $4$ out of $4 x^{2}$ .

$4 (x^{2}) - 4 x - 24 = 0$

Factor $4$ out of $- 4 x$ .

$4 (x^{2}) + 4 (- x) - 24 = 0$

Factor $4$ out of $- 24$ .

$4 (x^{2}) + 4 (- x) + 4 (- 6) = 0$

Factor $4$ out of $4 (x^{2}) + 4 (- x)$ .

$4 (x^{2} - x) + 4 (- 6) = 0$

Factor $4$ out of $4 (x^{2} - x) + 4 (- 6)$ .

$4 (x^{2} - x - 6) = 0$

Step 2

Factor.

Factor $x^{2} - x - 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

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

Remove unnecessary parentheses.

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

Step 3

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

$x - 3 = 0$

$x + 2 = 0$

Step 4

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 5

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 6

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

$x = 3, - 2$

Solve by Factoring 4x^2-4x-24=0

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