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

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


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

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

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

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

Combine like terms: 15x + -4x = 11x
2x(-20 + 11x + 3x2) = 0
(-20 * 2x + 11x * 2x + 3x2 * 2x) = 0
(-40x + 22x2 + 6x3) = 0

Solving
-40x + 22x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-20 + 11x + 3x2) = 0

Factor a trinomial.
2x((-5 + -1x)(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 '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -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, -5, 1.333333333}

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