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

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

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

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

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

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

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

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

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

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

Combine like terms: 1x + -1x = 0
-6 + -2x + 4x2 + -5(-1 + 0 + x2) = 2(x + -2)(x + -1)
-6 + -2x + 4x2 + -5(-1 + x2) = 2(x + -2)(x + -1)
-6 + -2x + 4x2 + (-1 * -5 + x2 * -5) = 2(x + -2)(x + -1)
-6 + -2x + 4x2 + (5 + -5x2) = 2(x + -2)(x + -1)

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

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

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

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

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

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

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

Solving
-1 + -2x + -1x2 = 4 + -6x + 2x2

Solving for variable 'x'.

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

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

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

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

Reorder the terms:
-5 + 4x + -3x2 = 4 + -4 + -6x + 6x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-5 + 4x + -3x2 = 0 + -6x + 6x + 2x2 + -2x2
-5 + 4x + -3x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
-5 + 4x + -3x2 = 0 + 2x2 + -2x2
-5 + 4x + -3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 4x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.666666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + -1.666666667
-1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-1.333333333x + x2 = -1.666666667

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -1.666666667 + 0.4444444442

Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228
0.4444444442 + -1.333333333x + x2 = -1.2222222228

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -1.2222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.