3x(x-20)(2x+5)=0

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Solution for 3x(x-20)(2x+5)=0 equation: 


Simplifying
3x(x + -20)(2x + 5) = 0

Reorder the terms:
3x(-20 + x)(2x + 5) = 0

Reorder the terms:
3x(-20 + x)(5 + 2x) = 0

Multiply (-20 + x) * (5 + 2x)
3x(-20(5 + 2x) + x(5 + 2x)) = 0
3x((5 * -20 + 2x * -20) + x(5 + 2x)) = 0
3x((-100 + -40x) + x(5 + 2x)) = 0
3x(-100 + -40x + (5 * x + 2x * x)) = 0
3x(-100 + -40x + (5x + 2x2)) = 0

Combine like terms: -40x + 5x = -35x
3x(-100 + -35x + 2x2) = 0
(-100 * 3x + -35x * 3x + 2x2 * 3x) = 0
(-300x + -105x2 + 6x3) = 0

Solving
-300x + -105x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-100 + -35x + 2x2) = 0

Factor a trinomial.
3x((-5 + -2x)(20 + -1x)) = 0

Ignore the factor 3.

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 + -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

Subproblem 3
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {0, -2.5, 20}

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