Solve by Factoring 3x^2+112=2x^2+22x

$3 x^{2} + 112 = 2 x^{2} + 22 x$

Step 1

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

Subtract $2 x^{2}$ from both sides of the equation.

$3 x^{2} + 112 - 2 x^{2} = 22 x$

Subtract $22 x$ from both sides of the equation.

$3 x^{2} + 112 - 2 x^{2} - 22 x = 0$

Step 2

Subtract $2 x^{2}$ from $3 x^{2}$ .

$x^{2} + 112 - 22 x = 0$

Step 3

Factor $x^{2} + 112 - 22 x$ 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 $112$ and whose sum is $- 22$ .

$- 14, - 8$

Write the factored form using these integers.

$(x - 14) (x - 8) = 0$

Step 4

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

$x - 14 = 0$

$x - 8 = 0$

Step 5

Set $x - 14$ equal to $0$ and solve for $x$ .

Set $x - 14$ equal to $0$ .

$x - 14 = 0$

Add $14$ to both sides of the equation.

$x = 14$

Step 6

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Step 7

The final solution is all the values that make $(x - 14) (x - 8) = 0$ true.

$x = 14, 8$

Solve by Factoring 3x^2+112=2x^2+22x

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