(3x-2)(3x-2)=6x-4

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Solution for (3x-2)(3x-2)=6x-4 equation: 


Simplifying
(3x + -2)(3x + -2) = 6x + -4

Reorder the terms:
(-2 + 3x)(3x + -2) = 6x + -4

Reorder the terms:
(-2 + 3x)(-2 + 3x) = 6x + -4

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

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

Reorder the terms:
4 + -12x + 9x2 = -4 + 6x

Solving
4 + -12x + 9x2 = -4 + 6x

Solving for variable 'x'.

Reorder the terms:
4 + 4 + -12x + -6x + 9x2 = -4 + 6x + 4 + -6x

Combine like terms: 4 + 4 = 8
8 + -12x + -6x + 9x2 = -4 + 6x + 4 + -6x

Combine like terms: -12x + -6x = -18x
8 + -18x + 9x2 = -4 + 6x + 4 + -6x

Reorder the terms:
8 + -18x + 9x2 = -4 + 4 + 6x + -6x

Combine like terms: -4 + 4 = 0
8 + -18x + 9x2 = 0 + 6x + -6x
8 + -18x + 9x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
8 + -18x + 9x2 = 0

Factor a trinomial.
(2 + -3x)(4 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0.6666666667, 1.333333333}

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