-5x(x-4)(2x-3)=0

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Solution for -5x(x-4)(2x-3)=0 equation: 


Simplifying
-5x(x + -4)(2x + -3) = 0

Reorder the terms:
-5x(-4 + x)(2x + -3) = 0

Reorder the terms:
-5x(-4 + x)(-3 + 2x) = 0

Multiply (-4 + x) * (-3 + 2x)
-5x(-4(-3 + 2x) + x(-3 + 2x)) = 0
-5x((-3 * -4 + 2x * -4) + x(-3 + 2x)) = 0
-5x((12 + -8x) + x(-3 + 2x)) = 0
-5x(12 + -8x + (-3 * x + 2x * x)) = 0
-5x(12 + -8x + (-3x + 2x2)) = 0

Combine like terms: -8x + -3x = -11x
-5x(12 + -11x + 2x2) = 0
(12 * -5x + -11x * -5x + 2x2 * -5x) = 0
(-60x + 55x2 + -10x3) = 0

Solving
-60x + 55x2 + -10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-12 + 11x + -2x2) = 0

Factor a trinomial.
5x((-4 + x)(3 + -2x)) = 0

Ignore the factor 5.

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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 4, 1.5}

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