4x(2x-10)(3x+5)=0

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Solution for 4x(2x-10)(3x+5)=0 equation: 


Simplifying
4x(2x + -10)(3x + 5) = 0

Reorder the terms:
4x(-10 + 2x)(3x + 5) = 0

Reorder the terms:
4x(-10 + 2x)(5 + 3x) = 0

Multiply (-10 + 2x) * (5 + 3x)
4x(-10(5 + 3x) + 2x * (5 + 3x)) = 0
4x((5 * -10 + 3x * -10) + 2x * (5 + 3x)) = 0
4x((-50 + -30x) + 2x * (5 + 3x)) = 0
4x(-50 + -30x + (5 * 2x + 3x * 2x)) = 0
4x(-50 + -30x + (10x + 6x2)) = 0

Combine like terms: -30x + 10x = -20x
4x(-50 + -20x + 6x2) = 0
(-50 * 4x + -20x * 4x + 6x2 * 4x) = 0
(-200x + -80x2 + 24x3) = 0

Solving
-200x + -80x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-25 + -10x + 3x2) = 0

Factor a trinomial.
8x((-5 + -3x)(5 + -1x)) = 0

Ignore the factor 8.

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 '(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
Solution
x = {0, -1.666666667, 5}

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