(3x-2)(3x-2)=49

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Solution for (3x-2)(3x-2)=49 equation: 


Simplifying
(3x + -2)(3x + -2) = 49

Reorder the terms:
(-2 + 3x)(3x + -2) = 49

Reorder the terms:
(-2 + 3x)(-2 + 3x) = 49

Multiply (-2 + 3x) * (-2 + 3x)
(-2(-2 + 3x) + 3x * (-2 + 3x)) = 49
((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 49
((4 + -6x) + 3x * (-2 + 3x)) = 49
(4 + -6x + (-2 * 3x + 3x * 3x)) = 49
(4 + -6x + (-6x + 9x2)) = 49

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) = 49

Solving
4 + -12x + 9x2 = 49

Solving for variable 'x'.

Reorder the terms:
4 + -49 + -12x + 9x2 = 49 + -49

Combine like terms: 4 + -49 = -45
-45 + -12x + 9x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-45 + -12x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -4x + 3x2) = 0

Factor a trinomial.
3((-5 + -3x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.666666667, 3}

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