(5x-1)(5x-1)=16

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Solution for (5x-1)(5x-1)=16 equation: 


Simplifying
(5x + -1)(5x + -1) = 16

Reorder the terms:
(-1 + 5x)(5x + -1) = 16

Reorder the terms:
(-1 + 5x)(-1 + 5x) = 16

Multiply (-1 + 5x) * (-1 + 5x)
(-1(-1 + 5x) + 5x * (-1 + 5x)) = 16
((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) = 16
((1 + -5x) + 5x * (-1 + 5x)) = 16
(1 + -5x + (-1 * 5x + 5x * 5x)) = 16
(1 + -5x + (-5x + 25x2)) = 16

Combine like terms: -5x + -5x = -10x
(1 + -10x + 25x2) = 16

Solving
1 + -10x + 25x2 = 16

Solving for variable 'x'.

Reorder the terms:
1 + -16 + -10x + 25x2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + -10x + 25x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + -10x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2x + 5x2) = 0

Factor a trinomial.
5((-3 + -5x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-0.6, 1}

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