Solve by Factoring 2x^2-6x=56

$2 x^{2} - 6 x = 56$

Step 1

Subtract $56$ from both sides of the equation.

$2 x^{2} - 6 x - 56 = 0$

Step 2

Factor $2$ out of $2 x^{2} - 6 x - 56$ .

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

$2 (x^{2}) - 6 x - 56 = 0$

Factor $2$ out of $- 6 x$ .

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

Factor $2$ out of $- 56$ .

$2 x^{2} + 2 (- 3 x) + 2 \cdot - 28 = 0$

Factor $2$ out of $2 x^{2} + 2 (- 3 x)$ .

$2 (x^{2} - 3 x) + 2 \cdot - 28 = 0$

Factor $2$ out of $2 (x^{2} - 3 x) + 2 \cdot - 28$ .

$2 (x^{2} - 3 x - 28) = 0$

Step 3

Factor.

Factor $x^{2} - 3 x - 28$ 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 $- 28$ and whose sum is $- 3$ .

$- 7, 4$

Write the factored form using these integers.

$2 ((x - 7) (x + 4)) = 0$

Remove unnecessary parentheses.

$2 (x - 7) (x + 4) = 0$

Step 4

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

$x - 7 = 0$

$x + 4 = 0$

Step 5

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

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

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Step 6

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

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 7

The final solution is all the values that make $2 (x - 7) (x + 4) = 0$ true.

$x = 7, - 4$

Solve by Factoring 2x^2-6x=56

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