9x(3x-2)(2x-1)=0

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Solution for 9x(3x-2)(2x-1)=0 equation:


Simplifying
9x(3x + -2)(2x + -1) = 0

Reorder the terms:
9x(-2 + 3x)(2x + -1) = 0

Reorder the terms:
9x(-2 + 3x)(-1 + 2x) = 0

Multiply (-2 + 3x) * (-1 + 2x)
9x(-2(-1 + 2x) + 3x * (-1 + 2x)) = 0
9x((-1 * -2 + 2x * -2) + 3x * (-1 + 2x)) = 0
9x((2 + -4x) + 3x * (-1 + 2x)) = 0
9x(2 + -4x + (-1 * 3x + 2x * 3x)) = 0
9x(2 + -4x + (-3x + 6x2)) = 0

Combine like terms: -4x + -3x = -7x
9x(2 + -7x + 6x2) = 0
(2 * 9x + -7x * 9x + 6x2 * 9x) = 0
(18x + -63x2 + 54x3) = 0

Solving
18x + -63x2 + 54x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(2 + -7x + 6x2) = 0

Factor a trinomial.
9x((1 + -2x)(2 + -3x)) = 0

Ignore the factor 9.

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 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {0, 0.5, 0.6666666667}

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