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

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


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

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

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

Multiply (-5 + 4x) * (-4 + 3x)
3x(-5(-4 + 3x) + 4x * (-4 + 3x)) = 0
3x((-4 * -5 + 3x * -5) + 4x * (-4 + 3x)) = 0
3x((20 + -15x) + 4x * (-4 + 3x)) = 0
3x(20 + -15x + (-4 * 4x + 3x * 4x)) = 0
3x(20 + -15x + (-16x + 12x2)) = 0

Combine like terms: -15x + -16x = -31x
3x(20 + -31x + 12x2) = 0
(20 * 3x + -31x * 3x + 12x2 * 3x) = 0
(60x + -93x2 + 36x3) = 0

Solving
60x + -93x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(20 + -31x + 12x2) = 0

Factor a trinomial.
3x((5 + -4x)(4 + -3x)) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

Subproblem 3
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, 1.25, 1.333333333}

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