(5x-1)(5x-1)=(5x-1)

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


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

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

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

Multiply (-1 + 5x) * (-1 + 5x)
(-1(-1 + 5x) + 5x * (-1 + 5x)) = (5x + -1)
((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = (5x + -1)
((1 + -5x) + 5x * (-1 + 5x)) = (5x + -1)
(1 + -5x + (-1 * 5x + 5x * 5x)) = (5x + -1)
(1 + -5x + (-5x + 25x2)) = (5x + -1)

Combine like terms: -5x + -5x = -10x
(1 + -10x + 25x2) = (5x + -1)

Reorder the terms:
1 + -10x + 25x2 = (-1 + 5x)

Remove parenthesis around (-1 + 5x)
1 + -10x + 25x2 = -1 + 5x

Solving
1 + -10x + 25x2 = -1 + 5x

Solving for variable 'x'.

Reorder the terms:
1 + 1 + -10x + -5x + 25x2 = -1 + 5x + 1 + -5x

Combine like terms: 1 + 1 = 2
2 + -10x + -5x + 25x2 = -1 + 5x + 1 + -5x

Combine like terms: -10x + -5x = -15x
2 + -15x + 25x2 = -1 + 5x + 1 + -5x

Reorder the terms:
2 + -15x + 25x2 = -1 + 1 + 5x + -5x

Combine like terms: -1 + 1 = 0
2 + -15x + 25x2 = 0 + 5x + -5x
2 + -15x + 25x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
2 + -15x + 25x2 = 0

Factor a trinomial.
(1 + -5x)(2 + -5x) = 0


Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

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

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

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {0.2, 0.4}

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