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

Solution for 12(x-5)(5x+1)=0 equation:

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

Reorder the terms:
12(-5 + x)(5x + 1) = 0

Reorder the terms:
12(-5 + x)(1 + 5x) = 0

Multiply (-5 + x) * (1 + 5x)
12(-5(1 + 5x) + x(1 + 5x)) = 0
12((1 * -5 + 5x * -5) + x(1 + 5x)) = 0
12((-5 + -25x) + x(1 + 5x)) = 0
12(-5 + -25x + (1 * x + 5x * x)) = 0
12(-5 + -25x + (1x + 5x2)) = 0

Combine like terms: -25x + 1x = -24x
12(-5 + -24x + 5x2) = 0
(-5 * 12 + -24x * 12 + 5x2 * 12) = 0
(-60 + -288x + 60x2) = 0

Solving
-60 + -288x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-5 + -24x + 5x2) = 0

Factor a trinomial.
12((-1 + -5x)(5 + -1x)) = 0

Ignore the factor 12.
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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.2, 5}