x^2+3x=-4(-2x+1)-2

Solution for x^2+3x=-4(-2x+1)-2 equation:

Simplifying
x2 + 3x = -4(-2x + 1) + -2

Reorder the terms:
3x + x2 = -4(-2x + 1) + -2

Reorder the terms:
3x + x2 = -4(1 + -2x) + -2
3x + x2 = (1 * -4 + -2x * -4) + -2
3x + x2 = (-4 + 8x) + -2

Reorder the terms:
3x + x2 = -4 + -2 + 8x

Combine like terms: -4 + -2 = -6
3x + x2 = -6 + 8x

Solving
3x + x2 = -6 + 8x

Solving for variable 'x'.

Reorder the terms:
6 + 3x + -8x + x2 = -6 + 8x + 6 + -8x

Combine like terms: 3x + -8x = -5x
6 + -5x + x2 = -6 + 8x + 6 + -8x

Reorder the terms:
6 + -5x + x2 = -6 + 6 + 8x + -8x

Combine like terms: -6 + 6 = 0
6 + -5x + x2 = 0 + 8x + -8x
6 + -5x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
6 + -5x + x2 = 0

Factor a trinomial.
(2 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}