x(x-1)(2x+3)=0

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Solution for x(x-1)(2x+3)=0 equation:


Simplifying
x(x + -1)(2x + 3) = 0

Reorder the terms:
x(-1 + x)(2x + 3) = 0

Reorder the terms:
x(-1 + x)(3 + 2x) = 0

Multiply (-1 + x) * (3 + 2x)
x(-1(3 + 2x) + x(3 + 2x)) = 0
x((3 * -1 + 2x * -1) + x(3 + 2x)) = 0
x((-3 + -2x) + x(3 + 2x)) = 0
x(-3 + -2x + (3 * x + 2x * x)) = 0
x(-3 + -2x + (3x + 2x2)) = 0

Combine like terms: -2x + 3x = 1x
x(-3 + 1x + 2x2) = 0
(-3 * x + 1x * x + 2x2 * x) = 0
(-3x + 1x2 + 2x3) = 0

Solving
-3x + 1x2 + 2x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((-3 + -2x)(1 + -1x)) = 0

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 '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

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, -1.5, 1}

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