(5x-1)*(5x-1)-10x+2=0

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Solution for (5x-1)*(5x-1)-10x+2=0 equation: 


Simplifying
(5x + -1)(5x + -1) + -10x + 2 = 0

Reorder the terms:
(-1 + 5x)(5x + -1) + -10x + 2 = 0

Reorder the terms:
(-1 + 5x)(-1 + 5x) + -10x + 2 = 0

Multiply (-1 + 5x) * (-1 + 5x)
(-1(-1 + 5x) + 5x * (-1 + 5x)) + -10x + 2 = 0
((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) + -10x + 2 = 0
((1 + -5x) + 5x * (-1 + 5x)) + -10x + 2 = 0
(1 + -5x + (-1 * 5x + 5x * 5x)) + -10x + 2 = 0
(1 + -5x + (-5x + 25x2)) + -10x + 2 = 0

Combine like terms: -5x + -5x = -10x
(1 + -10x + 25x2) + -10x + 2 = 0

Reorder the terms:
1 + 2 + -10x + -10x + 25x2 = 0

Combine like terms: 1 + 2 = 3
3 + -10x + -10x + 25x2 = 0

Combine like terms: -10x + -10x = -20x
3 + -20x + 25x2 = 0

Solving
3 + -20x + 25x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -5x)(3 + -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 '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0.2, 0.6}

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