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

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


Simplifying
(3x + -2)(3x + -2) = x2

Reorder the terms:
(-2 + 3x)(3x + -2) = x2

Reorder the terms:
(-2 + 3x)(-2 + 3x) = x2

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

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

Solving
4 + -12x + 9x2 = x2

Solving for variable 'x'.

Combine like terms: 9x2 + -1x2 = 8x2
4 + -12x + 8x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -12x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -3x + 2x2) = 0

Factor a trinomial.
4((1 + -2x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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 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 = {0.5, 1}

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