5(x-8)(5x+1)=0

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Solution for 5(x-8)(5x+1)=0 equation: 


Simplifying
5(x + -8)(5x + 1) = 0

Reorder the terms:
5(-8 + x)(5x + 1) = 0

Reorder the terms:
5(-8 + x)(1 + 5x) = 0

Multiply (-8 + x) * (1 + 5x)
5(-8(1 + 5x) + x(1 + 5x)) = 0
5((1 * -8 + 5x * -8) + x(1 + 5x)) = 0
5((-8 + -40x) + x(1 + 5x)) = 0
5(-8 + -40x + (1 * x + 5x * x)) = 0
5(-8 + -40x + (1x + 5x2)) = 0

Combine like terms: -40x + 1x = -39x
5(-8 + -39x + 5x2) = 0
(-8 * 5 + -39x * 5 + 5x2 * 5) = 0
(-40 + -195x + 25x2) = 0

Solving
-40 + -195x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -39x + 5x2) = 0

Factor a trinomial.
5((-1 + -5x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-0.2, 8}

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