(3x+1)(3x+1)=25

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Solution for (3x+1)(3x+1)=25 equation: 


Simplifying
(3x + 1)(3x + 1) = 25

Reorder the terms:
(1 + 3x)(3x + 1) = 25

Reorder the terms:
(1 + 3x)(1 + 3x) = 25

Multiply (1 + 3x) * (1 + 3x)
(1(1 + 3x) + 3x * (1 + 3x)) = 25
((1 * 1 + 3x * 1) + 3x * (1 + 3x)) = 25
((1 + 3x) + 3x * (1 + 3x)) = 25
(1 + 3x + (1 * 3x + 3x * 3x)) = 25
(1 + 3x + (3x + 9x2)) = 25

Combine like terms: 3x + 3x = 6x
(1 + 6x + 9x2) = 25

Solving
1 + 6x + 9x2 = 25

Solving for variable 'x'.

Reorder the terms:
1 + -25 + 6x + 9x2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 6x + 9x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 6x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 2x + 3x2) = 0

Factor a trinomial.
3((-2 + -1x)(4 + -3x)) = 0

Ignore the factor 3.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1.333333333}

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