(3x-5)(3x-5)-81=0

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Solution for (3x-5)(3x-5)-81=0 equation: 


Simplifying
(3x + -5)(3x + -5) + -81 = 0

Reorder the terms:
(-5 + 3x)(3x + -5) + -81 = 0

Reorder the terms:
(-5 + 3x)(-5 + 3x) + -81 = 0

Multiply (-5 + 3x) * (-5 + 3x)
(-5(-5 + 3x) + 3x * (-5 + 3x)) + -81 = 0
((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) + -81 = 0
((25 + -15x) + 3x * (-5 + 3x)) + -81 = 0
(25 + -15x + (-5 * 3x + 3x * 3x)) + -81 = 0
(25 + -15x + (-15x + 9x2)) + -81 = 0

Combine like terms: -15x + -15x = -30x
(25 + -30x + 9x2) + -81 = 0

Reorder the terms:
25 + -81 + -30x + 9x2 = 0

Combine like terms: 25 + -81 = -56
-56 + -30x + 9x2 = 0

Solving
-56 + -30x + 9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(14 + -3x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(14 + -3x)' equal to zero and attempt to solve:

Simplifying
14 + -3x = 0

Solving
14 + -3x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3x = 0 + -14
-3x = 0 + -14

Combine like terms: 0 + -14 = -14
-3x = -14

Divide each side by '-3'.
x = 4.666666667

Simplifying
x = 4.666666667
Solution
x = {-1.333333333, 4.666666667}

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