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

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


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

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

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

Remove parenthesis around (4x)
(-3 + x)(5 + 2x) * 4x = 0

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

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

Combine like terms: -6x + 5x = -1x
4x(-15 + -1x + 2x2) = 0
(-15 * 4x + -1x * 4x + 2x2 * 4x) = 0
(-60x + -4x2 + 8x3) = 0

Solving
-60x + -4x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-15 + -1x + 2x2) = 0

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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -2.5, 3}

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