Solve for x -2x^2+6x-28=4+2x-3x^2

$- 2 x^{2} + 6 x - 28 = 4 + 2 x - 3 x^{2}$

Step 1

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$- 2 x^{2} + 6 x - 28 - 2 x = 4 - 3 x^{2}$

Add $3 x^{2}$ to both sides of the equation.

$- 2 x^{2} + 6 x - 28 - 2 x + 3 x^{2} = 4$

Add $- 2 x^{2}$ and $3 x^{2}$ .

$x^{2} + 6 x - 28 - 2 x = 4$

Subtract $2 x$ from $6 x$ .

$x^{2} + 4 x - 28 = 4$

Step 2

Subtract $4$ from both sides of the equation.

$x^{2} + 4 x - 28 - 4 = 0$

Step 3

Subtract $4$ from $- 28$ .

$x^{2} + 4 x - 32 = 0$

Step 4

Factor $x^{2} + 4 x - 32$ 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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Write the factored form using these integers.

$(x - 4) (x + 8) = 0$

Step 5

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

$x - 4 = 0$

$x + 8 = 0$

Step 6

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

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

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 7

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

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

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 8

The final solution is all the values that make $(x - 4) (x + 8) = 0$ true.

$x = 4, - 8$

Solve for x -2x^2+6x-28=4+2x-3x^2

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