(3x+7)(3x+7)=4

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Solution for (3x+7)(3x+7)=4 equation: 


Simplifying
(3x + 7)(3x + 7) = 4

Reorder the terms:
(7 + 3x)(3x + 7) = 4

Reorder the terms:
(7 + 3x)(7 + 3x) = 4

Multiply (7 + 3x) * (7 + 3x)
(7(7 + 3x) + 3x * (7 + 3x)) = 4
((7 * 7 + 3x * 7) + 3x * (7 + 3x)) = 4
((49 + 21x) + 3x * (7 + 3x)) = 4
(49 + 21x + (7 * 3x + 3x * 3x)) = 4
(49 + 21x + (21x + 9x2)) = 4

Combine like terms: 21x + 21x = 42x
(49 + 42x + 9x2) = 4

Solving
49 + 42x + 9x2 = 4

Solving for variable 'x'.

Reorder the terms:
49 + -4 + 42x + 9x2 = 4 + -4

Combine like terms: 49 + -4 = 45
45 + 42x + 9x2 = 4 + -4

Combine like terms: 4 + -4 = 0
45 + 42x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 14x + 3x2) = 0

Factor a trinomial.
3((3 + x)(5 + 3x)) = 0

Ignore the factor 3.

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

Simplifying
3 + x = 0

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

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

Combine like terms: 0 + -3 = -3
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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