(3x+1)(3x+1)-100=0

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Solution for (3x+1)(3x+1)-100=0 equation: 


Simplifying
(3x + 1)(3x + 1) + -100 = 0

Reorder the terms:
(1 + 3x)(3x + 1) + -100 = 0

Reorder the terms:
(1 + 3x)(1 + 3x) + -100 = 0

Multiply (1 + 3x) * (1 + 3x)
(1(1 + 3x) + 3x * (1 + 3x)) + -100 = 0
((1 * 1 + 3x * 1) + 3x * (1 + 3x)) + -100 = 0
((1 + 3x) + 3x * (1 + 3x)) + -100 = 0
(1 + 3x + (1 * 3x + 3x * 3x)) + -100 = 0
(1 + 3x + (3x + 9x2)) + -100 = 0

Combine like terms: 3x + 3x = 6x
(1 + 6x + 9x2) + -100 = 0

Reorder the terms:
1 + -100 + 6x + 9x2 = 0

Combine like terms: 1 + -100 = -99
-99 + 6x + 9x2 = 0

Solving
-99 + 6x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-33 + 2x + 3x2) = 0

Factor a trinomial.
3((-11 + -3x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.666666667, 3}

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