(6X+1)*(6X+1)=81

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Solution for (6X+1)*(6X+1)=81 equation: 


Simplifying
(6X + 1)(6X + 1) = 81

Reorder the terms:
(1 + 6X)(6X + 1) = 81

Reorder the terms:
(1 + 6X)(1 + 6X) = 81

Multiply (1 + 6X) * (1 + 6X)
(1(1 + 6X) + 6X * (1 + 6X)) = 81
((1 * 1 + 6X * 1) + 6X * (1 + 6X)) = 81
((1 + 6X) + 6X * (1 + 6X)) = 81
(1 + 6X + (1 * 6X + 6X * 6X)) = 81
(1 + 6X + (6X + 36X2)) = 81

Combine like terms: 6X + 6X = 12X
(1 + 12X + 36X2) = 81

Solving
1 + 12X + 36X2 = 81

Solving for variable 'X'.

Reorder the terms:
1 + -81 + 12X + 36X2 = 81 + -81

Combine like terms: 1 + -81 = -80
-80 + 12X + 36X2 = 81 + -81

Combine like terms: 81 + -81 = 0
-80 + 12X + 36X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + 3X + 9X2) = 0

Factor a trinomial.
4((-5 + -3X)(4 + -3X)) = 0

Ignore the factor 4.

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 '(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
Solution
X = {-1.666666667, 1.333333333}

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