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

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


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

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

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

Multiply (-2 + x) * (5 + 3x)
4x(-2(5 + 3x) + x(5 + 3x)) = 0
4x((5 * -2 + 3x * -2) + x(5 + 3x)) = 0
4x((-10 + -6x) + x(5 + 3x)) = 0
4x(-10 + -6x + (5 * x + 3x * x)) = 0
4x(-10 + -6x + (5x + 3x2)) = 0

Combine like terms: -6x + 5x = -1x
4x(-10 + -1x + 3x2) = 0
(-10 * 4x + -1x * 4x + 3x2 * 4x) = 0
(-40x + -4x2 + 12x3) = 0

Solving
-40x + -4x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-10 + -1x + 3x2) = 0

Factor a trinomial.
4x((-5 + -3x)(2 + -1x)) = 0

Ignore the factor 4.

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 + -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

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, -1.666666667, 2}

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