Solve by Factoring 2w^2-16w=12w-48

$2 w^{2} - 16 w = 12 w - 48$

Step 1

Move all the expressions to the left side of the equation.

Subtract $12 w$ from both sides of the equation.

$2 w^{2} - 16 w - 12 w = - 48$

Add $48$ to both sides of the equation.

$2 w^{2} - 16 w - 12 w + 48 = 0$

Step 2

Subtract $12 w$ from $- 16 w$ .

$2 w^{2} - 28 w + 48 = 0$

Step 3

Factor $2$ out of $2 w^{2} - 28 w + 48$ .

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

$2 (w^{2}) - 28 w + 48 = 0$

Factor $2$ out of $- 28 w$ .

$2 (w^{2}) + 2 (- 14 w) + 48 = 0$

Factor $2$ out of $48$ .

$2 w^{2} + 2 (- 14 w) + 2 \cdot 24 = 0$

Factor $2$ out of $2 w^{2} + 2 (- 14 w)$ .

$2 (w^{2} - 14 w) + 2 \cdot 24 = 0$

Factor $2$ out of $2 (w^{2} - 14 w) + 2 \cdot 24$ .

$2 (w^{2} - 14 w + 24) = 0$

Step 4

Factor.

Factor $w^{2} - 14 w + 24$ 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 $24$ and whose sum is $- 14$ .

$- 12, - 2$

Write the factored form using these integers.

$2 ((w - 12) (w - 2)) = 0$

Remove unnecessary parentheses.

$2 (w - 12) (w - 2) = 0$

Step 5

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

$w - 12 = 0$

$w - 2 = 0$

Step 6

Set $w - 12$ equal to $0$ and solve for $w$ .

Set $w - 12$ equal to $0$ .

$w - 12 = 0$

Add $12$ to both sides of the equation.

$w = 12$

Step 7

Set $w - 2$ equal to $0$ and solve for $w$ .

Set $w - 2$ equal to $0$ .

$w - 2 = 0$

Add $2$ to both sides of the equation.

$w = 2$

Step 8

The final solution is all the values that make $2 (w - 12) (w - 2) = 0$ true.

$w = 12, 2$

Solve by Factoring 2w^2-16w=12w-48

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