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

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


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

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

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

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

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

Reorder the terms:
-1 + 4x2 = -1 + 5x

Add '1' to each side of the equation.
-1 + 1 + 4x2 = -1 + 1 + 5x

Combine like terms: -1 + 1 = 0
0 + 4x2 = -1 + 1 + 5x
4x2 = -1 + 1 + 5x

Combine like terms: -1 + 1 = 0
4x2 = 0 + 5x
4x2 = 5x

Solving
4x2 = 5x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 4x) = 0


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 '(-5 + 4x)' equal to zero and attempt to solve:

Simplifying
-5 + 4x = 0

Solving
-5 + 4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4x = 0 + 5
4x = 0 + 5

Combine like terms: 0 + 5 = 5
4x = 5

Divide each side by '4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {0, 1.25}

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