4x(5x-6)(x+4)=0

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Solution for 4x(5x-6)(x+4)=0 equation:


Simplifying
4x(5x + -6)(x + 4) = 0

Reorder the terms:
4x(-6 + 5x)(x + 4) = 0

Reorder the terms:
4x(-6 + 5x)(4 + x) = 0

Multiply (-6 + 5x) * (4 + x)
4x(-6(4 + x) + 5x * (4 + x)) = 0
4x((4 * -6 + x * -6) + 5x * (4 + x)) = 0
4x((-24 + -6x) + 5x * (4 + x)) = 0
4x(-24 + -6x + (4 * 5x + x * 5x)) = 0
4x(-24 + -6x + (20x + 5x2)) = 0

Combine like terms: -6x + 20x = 14x
4x(-24 + 14x + 5x2) = 0
(-24 * 4x + 14x * 4x + 5x2 * 4x) = 0
(-96x + 56x2 + 20x3) = 0

Solving
-96x + 56x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-24 + 14x + 5x2) = 0

Factor a trinomial.
4x((-4 + -1x)(6 + -5x)) = 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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 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 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 3

Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2

Solution

x = {0, -4, 1.2}

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