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

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


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

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

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

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

Combine like terms: -4x + 1x = -3x
3x(-2 + -3x + 2x2) = 0
(-2 * 3x + -3x * 3x + 2x2 * 3x) = 0
(-6x + -9x2 + 6x3) = 0

Solving
-6x + -9x2 + 6x3 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

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 '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 3

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

Solution

x = {0, -0.5, 2}

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