(3x-7)(3x-7)=64

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Solution for (3x-7)(3x-7)=64 equation:


Simplifying
(3x + -7)(3x + -7) = 64

Reorder the terms:
(-7 + 3x)(3x + -7) = 64

Reorder the terms:
(-7 + 3x)(-7 + 3x) = 64

Multiply (-7 + 3x) * (-7 + 3x)
(-7(-7 + 3x) + 3x * (-7 + 3x)) = 64
((-7 * -7 + 3x * -7) + 3x * (-7 + 3x)) = 64
((49 + -21x) + 3x * (-7 + 3x)) = 64
(49 + -21x + (-7 * 3x + 3x * 3x)) = 64
(49 + -21x + (-21x + 9x2)) = 64

Combine like terms: -21x + -21x = -42x
(49 + -42x + 9x2) = 64

Solving
49 + -42x + 9x2 = 64

Solving for variable 'x'.

Reorder the terms:
49 + -64 + -42x + 9x2 = 64 + -64

Combine like terms: 49 + -64 = -15
-15 + -42x + 9x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-15 + -42x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -14x + 3x2) = 0

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

Ignore the factor 3.

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.3333333333, 5}

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