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

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

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

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

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

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

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

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

Combine like terms: 1x + -1x = 0
3 + -5x + 2x2 + -1(1 + 0 + -1x2) = -4(x + 1)(x + -1)
3 + -5x + 2x2 + -1(1 + -1x2) = -4(x + 1)(x + -1)
3 + -5x + 2x2 + (1 * -1 + -1x2 * -1) = -4(x + 1)(x + -1)
3 + -5x + 2x2 + (-1 + 1x2) = -4(x + 1)(x + -1)

Reorder the terms:
3 + -1 + -5x + 2x2 + 1x2 = -4(x + 1)(x + -1)

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

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

Reorder the terms:
2 + -5x + 3x2 = -4(1 + x)(x + -1)

Reorder the terms:
2 + -5x + 3x2 = -4(1 + x)(-1 + x)

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

Combine like terms: 1x + -1x = 0
2 + -5x + 3x2 = -4(-1 + 0 + x2)
2 + -5x + 3x2 = -4(-1 + x2)
2 + -5x + 3x2 = (-1 * -4 + x2 * -4)
2 + -5x + 3x2 = (4 + -4x2)

Solving
2 + -5x + 3x2 = 4 + -4x2

Solving for variable 'x'.

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

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

Combine like terms: 3x2 + 4x2 = 7x2
-2 + -5x + 7x2 = 4 + -4x2 + -4 + 4x2

Reorder the terms:
-2 + -5x + 7x2 = 4 + -4 + -4x2 + 4x2

Combine like terms: 4 + -4 = 0
-2 + -5x + 7x2 = 0 + -4x2 + 4x2
-2 + -5x + 7x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-2 + -5x + 7x2 = 0

Factor a trinomial.
(-2 + -7x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-2 + -7x)' equal to zero and attempt to solve:

Simplifying
-2 + -7x = 0

Solving
-2 + -7x = 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 + -7x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7x = 0 + 2
-7x = 0 + 2

Combine like terms: 0 + 2 = 2
-7x = 2

Divide each side by '-7'.
x = -0.2857142857

Simplifying
x = -0.2857142857
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.2857142857, 1}