2(x^2-1)-8x(x-1)=0

Solution for 2(x^2-1)-8x(x-1)=0 equation:

Simplifying
2(x2 + -1) + -8x(x + -1) = 0

Reorder the terms:
2(-1 + x2) + -8x(x + -1) = 0
(-1 * 2 + x2 * 2) + -8x(x + -1) = 0
(-2 + 2x2) + -8x(x + -1) = 0

Reorder the terms:
-2 + 2x2 + -8x(-1 + x) = 0
-2 + 2x2 + (-1 * -8x + x * -8x) = 0
-2 + 2x2 + (8x + -8x2) = 0

Reorder the terms:
-2 + 8x + 2x2 + -8x2 = 0

Combine like terms: 2x2 + -8x2 = -6x2
-2 + 8x + -6x2 = 0

Solving
-2 + 8x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4x + -3x2) = 0

Factor a trinomial.
2((-1 + x)(1 + -3x)) = 0

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

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {1, 0.3333333333}