2x(3x-4)(5x+6)=

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Solution for 2x(3x-4)(5x+6)= equation: 


Simplifying
2x(3x + -4)(5x + 6) = 0

Reorder the terms:
2x(-4 + 3x)(5x + 6) = 0

Reorder the terms:
2x(-4 + 3x)(6 + 5x) = 0

Multiply (-4 + 3x) * (6 + 5x)
2x(-4(6 + 5x) + 3x * (6 + 5x)) = 0
2x((6 * -4 + 5x * -4) + 3x * (6 + 5x)) = 0
2x((-24 + -20x) + 3x * (6 + 5x)) = 0
2x(-24 + -20x + (6 * 3x + 5x * 3x)) = 0
2x(-24 + -20x + (18x + 15x2)) = 0

Combine like terms: -20x + 18x = -2x
2x(-24 + -2x + 15x2) = 0
(-24 * 2x + -2x * 2x + 15x2 * 2x) = 0
(-48x + -4x2 + 30x3) = 0

Solving
-48x + -4x2 + 30x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-24 + -2x + 15x2) = 0

Factor a trinomial.
2x((-6 + -5x)(4 + -3x)) = 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 '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2

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, -1.2, 1.333333333}

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