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

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


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

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

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

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

Multiply (3 + 2x) * (3 + 2x)
x(3(3 + 2x) + 2x * (3 + 2x)) = 0
x((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 0
x((9 + 6x) + 2x * (3 + 2x)) = 0
x(9 + 6x + (3 * 2x + 2x * 2x)) = 0
x(9 + 6x + (6x + 4x2)) = 0

Combine like terms: 6x + 6x = 12x
x(9 + 12x + 4x2) = 0
(9 * x + 12x * x + 4x2 * x) = 0
(9x + 12x2 + 4x3) = 0

Solving
9x + 12x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + 12x + 4x2) = 0

Factor a trinomial.
x((3 + 2x)(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 '(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 '(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, -1.5, -1.5}

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