4x^2-1=2x-1

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

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

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

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

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

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

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

Solving
4x2 = 2x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + 2x) = 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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

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

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}