(3x+4)*(4x+5)*(3x)=

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Solution for (3x+4)*(4x+5)*(3x)= equation: 


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

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

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

Remove parenthesis around (3x)
(4 + 3x)(5 + 4x) * 3x = 0

Reorder the terms for easier multiplication:
3x(4 + 3x)(5 + 4x) = 0

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

Combine like terms: 16x + 15x = 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((4 + 3x)(5 + 4x)) = 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 '(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

Subproblem 3
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
Solution
x = {0, -1.333333333, -1.25}

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