(3x-9)(3x-9)=1

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Solution for (3x-9)(3x-9)=1 equation: 


Simplifying
(3x + -9)(3x + -9) = 1

Reorder the terms:
(-9 + 3x)(3x + -9) = 1

Reorder the terms:
(-9 + 3x)(-9 + 3x) = 1

Multiply (-9 + 3x) * (-9 + 3x)
(-9(-9 + 3x) + 3x * (-9 + 3x)) = 1
((-9 * -9 + 3x * -9) + 3x * (-9 + 3x)) = 1
((81 + -27x) + 3x * (-9 + 3x)) = 1
(81 + -27x + (-9 * 3x + 3x * 3x)) = 1
(81 + -27x + (-27x + 9x2)) = 1

Combine like terms: -27x + -27x = -54x
(81 + -54x + 9x2) = 1

Solving
81 + -54x + 9x2 = 1

Solving for variable 'x'.

Reorder the terms:
81 + -1 + -54x + 9x2 = 1 + -1

Combine like terms: 81 + -1 = 80
80 + -54x + 9x2 = 1 + -1

Combine like terms: 1 + -1 = 0
80 + -54x + 9x2 = 0

Factor a trinomial.
(8 + -3x)(10 + -3x) = 0


Subproblem 1
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {2.666666667, 3.333333333}

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