(3x-2)(3x-2)=x

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


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

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

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

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

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) = x

Solving
4 + -12x + 9x2 = x

Solving for variable 'x'.

Reorder the terms:
4 + -12x + -1x + 9x2 = x + -1x

Combine like terms: -12x + -1x = -13x
4 + -13x + 9x2 = x + -1x

Combine like terms: x + -1x = 0
4 + -13x + 9x2 = 0

Factor a trinomial.
(4 + -9x)(1 + -1x) = 0

Subproblem 1

Set the factor '(4 + -9x)' equal to zero and attempt to solve: Simplifying 4 + -9x = 0 Solving 4 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -9x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9x = 0 + -4 -9x = 0 + -4 Combine like terms: 0 + -4 = -4 -9x = -4 Divide each side by '-9'. x = 0.4444444444 Simplifying x = 0.4444444444

Subproblem 2

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 = {0.4444444444, 1}

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