2x(5x-9)(3x-4)=0

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Solution for 2x(5x-9)(3x-4)=0 equation: 


Simplifying
2x(5x + -9)(3x + -4) = 0

Reorder the terms:
2x(-9 + 5x)(3x + -4) = 0

Reorder the terms:
2x(-9 + 5x)(-4 + 3x) = 0

Multiply (-9 + 5x) * (-4 + 3x)
2x(-9(-4 + 3x) + 5x * (-4 + 3x)) = 0
2x((-4 * -9 + 3x * -9) + 5x * (-4 + 3x)) = 0
2x((36 + -27x) + 5x * (-4 + 3x)) = 0
2x(36 + -27x + (-4 * 5x + 3x * 5x)) = 0
2x(36 + -27x + (-20x + 15x2)) = 0

Combine like terms: -27x + -20x = -47x
2x(36 + -47x + 15x2) = 0
(36 * 2x + -47x * 2x + 15x2 * 2x) = 0
(72x + -94x2 + 30x3) = 0

Solving
72x + -94x2 + 30x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(36 + -47x + 15x2) = 0

Factor a trinomial.
2x((4 + -3x)(9 + -5x)) = 0

Ignore the factor 2.

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 '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {0, 1.333333333, 1.8}

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