(3x+1)*(3x+1)-49=0

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Solution for (3x+1)*(3x+1)-49=0 equation:


Simplifying
(3x + 1)(3x + 1) + -49 = 0

Reorder the terms:
(1 + 3x)(3x + 1) + -49 = 0

Reorder the terms:
(1 + 3x)(1 + 3x) + -49 = 0

Multiply (1 + 3x) * (1 + 3x)
(1(1 + 3x) + 3x * (1 + 3x)) + -49 = 0
((1 * 1 + 3x * 1) + 3x * (1 + 3x)) + -49 = 0
((1 + 3x) + 3x * (1 + 3x)) + -49 = 0
(1 + 3x + (1 * 3x + 3x * 3x)) + -49 = 0
(1 + 3x + (3x + 9x2)) + -49 = 0

Combine like terms: 3x + 3x = 6x
(1 + 6x + 9x2) + -49 = 0

Reorder the terms:
1 + -49 + 6x + 9x2 = 0

Combine like terms: 1 + -49 = -48
-48 + 6x + 9x2 = 0

Solving
-48 + 6x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 2x + 3x2) = 0

Factor a trinomial.
3((-8 + -3x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
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
Solution
x = {-2.666666667, 2}

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