(3x+1)(3x+1)=64

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Solution for (3x+1)(3x+1)=64 equation: 


Simplifying
(3x + 1)(3x + 1) = 64

Reorder the terms:
(1 + 3x)(3x + 1) = 64

Reorder the terms:
(1 + 3x)(1 + 3x) = 64

Multiply (1 + 3x) * (1 + 3x)
(1(1 + 3x) + 3x * (1 + 3x)) = 64
((1 * 1 + 3x * 1) + 3x * (1 + 3x)) = 64
((1 + 3x) + 3x * (1 + 3x)) = 64
(1 + 3x + (1 * 3x + 3x * 3x)) = 64
(1 + 3x + (3x + 9x2)) = 64

Combine like terms: 3x + 3x = 6x
(1 + 6x + 9x2) = 64

Solving
1 + 6x + 9x2 = 64

Solving for variable 'x'.

Reorder the terms:
1 + -64 + 6x + 9x2 = 64 + -64

Combine like terms: 1 + -64 = -63
-63 + 6x + 9x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-63 + 6x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 2x + 3x2) = 0

Factor a trinomial.
3((-3 + -1x)(7 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-3, 2.333333333}

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