(3x+7)(3x+7)=-6x-14

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Solution for (3x+7)(3x+7)=-6x-14 equation: 


Simplifying
(3x + 7)(3x + 7) = -6x + -14

Reorder the terms:
(7 + 3x)(3x + 7) = -6x + -14

Reorder the terms:
(7 + 3x)(7 + 3x) = -6x + -14

Multiply (7 + 3x) * (7 + 3x)
(7(7 + 3x) + 3x * (7 + 3x)) = -6x + -14
((7 * 7 + 3x * 7) + 3x * (7 + 3x)) = -6x + -14
((49 + 21x) + 3x * (7 + 3x)) = -6x + -14
(49 + 21x + (7 * 3x + 3x * 3x)) = -6x + -14
(49 + 21x + (21x + 9x2)) = -6x + -14

Combine like terms: 21x + 21x = 42x
(49 + 42x + 9x2) = -6x + -14

Reorder the terms:
49 + 42x + 9x2 = -14 + -6x

Solving
49 + 42x + 9x2 = -14 + -6x

Solving for variable 'x'.

Reorder the terms:
49 + 14 + 42x + 6x + 9x2 = -14 + -6x + 14 + 6x

Combine like terms: 49 + 14 = 63
63 + 42x + 6x + 9x2 = -14 + -6x + 14 + 6x

Combine like terms: 42x + 6x = 48x
63 + 48x + 9x2 = -14 + -6x + 14 + 6x

Reorder the terms:
63 + 48x + 9x2 = -14 + 14 + -6x + 6x

Combine like terms: -14 + 14 = 0
63 + 48x + 9x2 = 0 + -6x + 6x
63 + 48x + 9x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
63 + 48x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + 16x + 3x2) = 0

Factor a trinomial.
3((3 + x)(7 + 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 '(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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