(x+2)(2x-3)=5x^2+x-114

Solution for (x+2)(2x-3)=5x^2+x-114 equation:

Simplifying
(x + 2)(2x + -3) = 5x2 + x + -114

Reorder the terms:
(2 + x)(2x + -3) = 5x2 + x + -114

Reorder the terms:
(2 + x)(-3 + 2x) = 5x2 + x + -114

Multiply (2 + x) * (-3 + 2x)
(2(-3 + 2x) + x(-3 + 2x)) = 5x2 + x + -114
((-3 * 2 + 2x * 2) + x(-3 + 2x)) = 5x2 + x + -114
((-6 + 4x) + x(-3 + 2x)) = 5x2 + x + -114
(-6 + 4x + (-3 * x + 2x * x)) = 5x2 + x + -114
(-6 + 4x + (-3x + 2x2)) = 5x2 + x + -114

Combine like terms: 4x + -3x = 1x
(-6 + 1x + 2x2) = 5x2 + x + -114

Reorder the terms:
-6 + 1x + 2x2 = -114 + x + 5x2

Solving
-6 + 1x + 2x2 = -114 + x + 5x2

Solving for variable 'x'.

Reorder the terms:
-6 + 114 + 1x + -1x + 2x2 + -5x2 = -114 + x + 5x2 + 114 + -1x + -5x2

Combine like terms: -6 + 114 = 108
108 + 1x + -1x + 2x2 + -5x2 = -114 + x + 5x2 + 114 + -1x + -5x2

Combine like terms: 1x + -1x = 0
108 + 0 + 2x2 + -5x2 = -114 + x + 5x2 + 114 + -1x + -5x2
108 + 2x2 + -5x2 = -114 + x + 5x2 + 114 + -1x + -5x2

Combine like terms: 2x2 + -5x2 = -3x2
108 + -3x2 = -114 + x + 5x2 + 114 + -1x + -5x2

Reorder the terms:
108 + -3x2 = -114 + 114 + x + -1x + 5x2 + -5x2

Combine like terms: -114 + 114 = 0
108 + -3x2 = 0 + x + -1x + 5x2 + -5x2
108 + -3x2 = x + -1x + 5x2 + -5x2

Combine like terms: x + -1x = 0
108 + -3x2 = 0 + 5x2 + -5x2
108 + -3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
108 + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + -1x2) = 0

Factor a difference between two squares.
3((6 + x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-6, 6}