(x+3)(2x-2)=(2x-1)(x+5)+4

Solution for (x+3)(2x-2)=(2x-1)(x+5)+4 equation:

Simplifying
(x + 3)(2x + -2) = (2x + -1)(x + 5) + 4

Reorder the terms:
(3 + x)(2x + -2) = (2x + -1)(x + 5) + 4

Reorder the terms:
(3 + x)(-2 + 2x) = (2x + -1)(x + 5) + 4

Multiply (3 + x) * (-2 + 2x)
(3(-2 + 2x) + x(-2 + 2x)) = (2x + -1)(x + 5) + 4
((-2 * 3 + 2x * 3) + x(-2 + 2x)) = (2x + -1)(x + 5) + 4
((-6 + 6x) + x(-2 + 2x)) = (2x + -1)(x + 5) + 4
(-6 + 6x + (-2 * x + 2x * x)) = (2x + -1)(x + 5) + 4
(-6 + 6x + (-2x + 2x2)) = (2x + -1)(x + 5) + 4

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

Reorder the terms:
-6 + 4x + 2x2 = (-1 + 2x)(x + 5) + 4

Reorder the terms:
-6 + 4x + 2x2 = (-1 + 2x)(5 + x) + 4

Multiply (-1 + 2x) * (5 + x)
-6 + 4x + 2x2 = (-1(5 + x) + 2x * (5 + x)) + 4
-6 + 4x + 2x2 = ((5 * -1 + x * -1) + 2x * (5 + x)) + 4
-6 + 4x + 2x2 = ((-5 + -1x) + 2x * (5 + x)) + 4
-6 + 4x + 2x2 = (-5 + -1x + (5 * 2x + x * 2x)) + 4
-6 + 4x + 2x2 = (-5 + -1x + (10x + 2x2)) + 4

Combine like terms: -1x + 10x = 9x
-6 + 4x + 2x2 = (-5 + 9x + 2x2) + 4

Reorder the terms:
-6 + 4x + 2x2 = -5 + 4 + 9x + 2x2

Combine like terms: -5 + 4 = -1
-6 + 4x + 2x2 = -1 + 9x + 2x2

Add '-2x2' to each side of the equation.
-6 + 4x + 2x2 + -2x2 = -1 + 9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 4x + 0 = -1 + 9x + 2x2 + -2x2
-6 + 4x = -1 + 9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 4x = -1 + 9x + 0
-6 + 4x = -1 + 9x

Solving
-6 + 4x = -1 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
-6 + 4x + -9x = -1 + 9x + -9x

Combine like terms: 4x + -9x = -5x
-6 + -5x = -1 + 9x + -9x

Combine like terms: 9x + -9x = 0
-6 + -5x = -1 + 0
-6 + -5x = -1

Add '6' to each side of the equation.
-6 + 6 + -5x = -1 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = -1 + 6
-5x = -1 + 6

Combine like terms: -1 + 6 = 5
-5x = 5

Divide each side by '-5'.
x = -1

Simplifying
x = -1