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

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


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

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

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

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

Combine like terms: -3x + 20x = 17x
2x(-15 + 17x + 4x2) = 0
(-15 * 2x + 17x * 2x + 4x2 * 2x) = 0
(-30x + 34x2 + 8x3) = 0

Solving
-30x + 34x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-15 + 17x + 4x2) = 0

Factor a trinomial.
2x((-5 + -1x)(3 + -4x)) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0, -5, 0.75}

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