2x^2-1=4x-1

Solution for 2x^2-1=4x-1 equation:

Simplifying
2x2 + -1 = 4x + -1

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

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

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

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

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

Solving
2x2 = 4x

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2
Solution
x = {0, 2}