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

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


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

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

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

Multiply (3 + 2x) * (-4 + 3x)
5x(3(-4 + 3x) + 2x * (-4 + 3x)) = 0
5x((-4 * 3 + 3x * 3) + 2x * (-4 + 3x)) = 0
5x((-12 + 9x) + 2x * (-4 + 3x)) = 0
5x(-12 + 9x + (-4 * 2x + 3x * 2x)) = 0
5x(-12 + 9x + (-8x + 6x2)) = 0

Combine like terms: 9x + -8x = 1x
5x(-12 + 1x + 6x2) = 0
(-12 * 5x + 1x * 5x + 6x2 * 5x) = 0
(-60x + 5x2 + 30x3) = 0

Solving
-60x + 5x2 + 30x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-12 + x + 6x2) = 0

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

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, -1.5, 1.333333333}

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