6x(2x-5)(x+5)=0

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Solution for 6x(2x-5)(x+5)=0 equation: 


Simplifying
6x(2x + -5)(x + 5) = 0

Reorder the terms:
6x(-5 + 2x)(x + 5) = 0

Reorder the terms:
6x(-5 + 2x)(5 + x) = 0

Multiply (-5 + 2x) * (5 + x)
6x(-5(5 + x) + 2x * (5 + x)) = 0
6x((5 * -5 + x * -5) + 2x * (5 + x)) = 0
6x((-25 + -5x) + 2x * (5 + x)) = 0
6x(-25 + -5x + (5 * 2x + x * 2x)) = 0
6x(-25 + -5x + (10x + 2x2)) = 0

Combine like terms: -5x + 10x = 5x
6x(-25 + 5x + 2x2) = 0
(-25 * 6x + 5x * 6x + 2x2 * 6x) = 0
(-150x + 30x2 + 12x3) = 0

Solving
-150x + 30x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-25 + 5x + 2x2) = 0

Factor a trinomial.
6x((-5 + -1x)(5 + -2x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Subproblem 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, -5, 2.5}

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