(2x-3)(x-1)=6+2(x+2)(x+3)

Solution for (2x-3)(x-1)=6+2(x+2)(x+3) equation:

Simplifying
(2x + -3)(x + -1) = 6 + 2(x + 2)(x + 3)

Reorder the terms:
(-3 + 2x)(x + -1) = 6 + 2(x + 2)(x + 3)

Reorder the terms:
(-3 + 2x)(-1 + x) = 6 + 2(x + 2)(x + 3)

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

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

Reorder the terms:
3 + -5x + 2x2 = 6 + 2(2 + x)(x + 3)

Reorder the terms:
3 + -5x + 2x2 = 6 + 2(2 + x)(3 + x)

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

Combine like terms: 2x + 3x = 5x
3 + -5x + 2x2 = 6 + 2(6 + 5x + x2)
3 + -5x + 2x2 = 6 + (6 * 2 + 5x * 2 + x2 * 2)
3 + -5x + 2x2 = 6 + (12 + 10x + 2x2)

Combine like terms: 6 + 12 = 18
3 + -5x + 2x2 = 18 + 10x + 2x2

Add '-2x2' to each side of the equation.
3 + -5x + 2x2 + -2x2 = 18 + 10x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + -5x + 0 = 18 + 10x + 2x2 + -2x2
3 + -5x = 18 + 10x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + -5x = 18 + 10x + 0
3 + -5x = 18 + 10x

Solving
3 + -5x = 18 + 10x

Solving for variable 'x'.

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

Add '-10x' to each side of the equation.
3 + -5x + -10x = 18 + 10x + -10x

Combine like terms: -5x + -10x = -15x
3 + -15x = 18 + 10x + -10x

Combine like terms: 10x + -10x = 0
3 + -15x = 18 + 0
3 + -15x = 18

Add '-3' to each side of the equation.
3 + -3 + -15x = 18 + -3

Combine like terms: 3 + -3 = 0
0 + -15x = 18 + -3
-15x = 18 + -3

Combine like terms: 18 + -3 = 15
-15x = 15

Divide each side by '-15'.
x = -1

Simplifying
x = -1