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

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


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

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

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

Multiply (-5 + 3x) * (3 + 4x)
3x(-5(3 + 4x) + 3x * (3 + 4x)) = 0
3x((3 * -5 + 4x * -5) + 3x * (3 + 4x)) = 0
3x((-15 + -20x) + 3x * (3 + 4x)) = 0
3x(-15 + -20x + (3 * 3x + 4x * 3x)) = 0
3x(-15 + -20x + (9x + 12x2)) = 0

Combine like terms: -20x + 9x = -11x
3x(-15 + -11x + 12x2) = 0
(-15 * 3x + -11x * 3x + 12x2 * 3x) = 0
(-45x + -33x2 + 36x3) = 0

Solving
-45x + -33x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-15 + -11x + 12x2) = 0

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

Simplifying
-3 + -4x = 0

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

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

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

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 3
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, -0.75, 1.666666667}

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