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

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


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

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

Multiply (3 + 2x) * (2 + -1x)
x(3(2 + -1x) + 2x * (2 + -1x)) = 0
x((2 * 3 + -1x * 3) + 2x * (2 + -1x)) = 0
x((6 + -3x) + 2x * (2 + -1x)) = 0
x(6 + -3x + (2 * 2x + -1x * 2x)) = 0
x(6 + -3x + (4x + -2x2)) = 0

Combine like terms: -3x + 4x = 1x
x(6 + 1x + -2x2) = 0
(6 * x + 1x * x + -2x2 * x) = 0
(6x + 1x2 + -2x3) = 0

Solving
6x + 1x2 + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + x + -2x2) = 0

Factor a trinomial.
x((2 + -1x)(3 + 2x)) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 3

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

Solution

x = {0, 2, -1.5}

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