(3x+2)(3x+2)-49=0

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Solution for (3x+2)(3x+2)-49=0 equation: 


Simplifying
(3x + 2)(3x + 2) + -49 = 0

Reorder the terms:
(2 + 3x)(3x + 2) + -49 = 0

Reorder the terms:
(2 + 3x)(2 + 3x) + -49 = 0

Multiply (2 + 3x) * (2 + 3x)
(2(2 + 3x) + 3x * (2 + 3x)) + -49 = 0
((2 * 2 + 3x * 2) + 3x * (2 + 3x)) + -49 = 0
((4 + 6x) + 3x * (2 + 3x)) + -49 = 0
(4 + 6x + (2 * 3x + 3x * 3x)) + -49 = 0
(4 + 6x + (6x + 9x2)) + -49 = 0

Combine like terms: 6x + 6x = 12x
(4 + 12x + 9x2) + -49 = 0

Reorder the terms:
4 + -49 + 12x + 9x2 = 0

Combine like terms: 4 + -49 = -45
-45 + 12x + 9x2 = 0

Solving
-45 + 12x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 4x + 3x2) = 0

Factor a trinomial.
3((-3 + -1x)(5 + -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 '(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
Solution
x = {-3, 1.666666667}

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