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

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


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

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

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

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

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

Add '-4' to each side of the equation.
4 + -12x + -4 + 9x2 = 4 + -4

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

Combine like terms: 4 + -4 = 0
0 + -12x + 9x2 = 4 + -4
-12x + 9x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-12x + 9x2 = 0

Solving
-12x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + 3x) = 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 '(-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, 1.333333333}

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