12=2((3x-7)(3x-7))+4

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Solution for 12=2((3x-7)(3x-7))+4 equation: 


Simplifying
12 = 2((3x + -7)(3x + -7)) + 4

Reorder the terms:
12 = 2((-7 + 3x)(3x + -7)) + 4

Reorder the terms:
12 = 2((-7 + 3x)(-7 + 3x)) + 4

Multiply (-7 + 3x) * (-7 + 3x)
12 = 2((-7(-7 + 3x) + 3x * (-7 + 3x))) + 4
12 = 2(((-7 * -7 + 3x * -7) + 3x * (-7 + 3x))) + 4
12 = 2(((49 + -21x) + 3x * (-7 + 3x))) + 4
12 = 2((49 + -21x + (-7 * 3x + 3x * 3x))) + 4
12 = 2((49 + -21x + (-21x + 9x2))) + 4

Combine like terms: -21x + -21x = -42x
12 = 2((49 + -42x + 9x2)) + 4
12 = (49 * 2 + -42x * 2 + 9x2 * 2) + 4
12 = (98 + -84x + 18x2) + 4

Reorder the terms:
12 = 98 + 4 + -84x + 18x2

Combine like terms: 98 + 4 = 102
12 = 102 + -84x + 18x2

Solving
12 = 102 + -84x + 18x2

Solving for variable 'x'.

Combine like terms: 12 + -102 = -90
-90 + 84x + -18x2 = 102 + -84x + 18x2 + -102 + 84x + -18x2

Reorder the terms:
-90 + 84x + -18x2 = 102 + -102 + -84x + 84x + 18x2 + -18x2

Combine like terms: 102 + -102 = 0
-90 + 84x + -18x2 = 0 + -84x + 84x + 18x2 + -18x2
-90 + 84x + -18x2 = -84x + 84x + 18x2 + -18x2

Combine like terms: -84x + 84x = 0
-90 + 84x + -18x2 = 0 + 18x2 + -18x2
-90 + 84x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
-90 + 84x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 14x + -3x2) = 0

Factor a trinomial.
6((-3 + x)(5 + -3x)) = 0

Ignore the factor 6.

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

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3

Subproblem 2
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
Solution
x = {3, 1.666666667}

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