4x(x-1)(2x+5)=0

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Solution for 4x(x-1)(2x+5)=0 equation:


Simplifying
4x(x + -1)(2x + 5) = 0

Reorder the terms:
4x(-1 + x)(2x + 5) = 0

Reorder the terms:
4x(-1 + x)(5 + 2x) = 0

Multiply (-1 + x) * (5 + 2x)
4x(-1(5 + 2x) + x(5 + 2x)) = 0
4x((5 * -1 + 2x * -1) + x(5 + 2x)) = 0
4x((-5 + -2x) + x(5 + 2x)) = 0
4x(-5 + -2x + (5 * x + 2x * x)) = 0
4x(-5 + -2x + (5x + 2x2)) = 0

Combine like terms: -2x + 5x = 3x
4x(-5 + 3x + 2x2) = 0
(-5 * 4x + 3x * 4x + 2x2 * 4x) = 0
(-20x + 12x2 + 8x3) = 0

Solving
-20x + 12x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-5 + 3x + 2x2) = 0

Factor a trinomial.
4x((-5 + -2x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {0, -2.5, 1}

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