(5x-5)(5x+1)=0

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


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

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

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

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

Combine like terms: -25x + 5x = -20x
(-5 + -20x + 25x2) = 0

Solving
-5 + -20x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + -4x + 5x2) = 0

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

Ignore the factor 5.

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 '(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 = {-0.2, 1}

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