(3x+1)(3x+7)=-9

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Solution for (3x+1)(3x+7)=-9 equation: 


Simplifying
(3x + 1)(3x + 7) = -9

Reorder the terms:
(1 + 3x)(3x + 7) = -9

Reorder the terms:
(1 + 3x)(7 + 3x) = -9

Multiply (1 + 3x) * (7 + 3x)
(1(7 + 3x) + 3x * (7 + 3x)) = -9
((7 * 1 + 3x * 1) + 3x * (7 + 3x)) = -9
((7 + 3x) + 3x * (7 + 3x)) = -9
(7 + 3x + (7 * 3x + 3x * 3x)) = -9
(7 + 3x + (21x + 9x2)) = -9

Combine like terms: 3x + 21x = 24x
(7 + 24x + 9x2) = -9

Solving
7 + 24x + 9x2 = -9

Solving for variable 'x'.

Reorder the terms:
7 + 9 + 24x + 9x2 = -9 + 9

Combine like terms: 7 + 9 = 16
16 + 24x + 9x2 = -9 + 9

Combine like terms: -9 + 9 = 0
16 + 24x + 9x2 = 0

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


Subproblem 1
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

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 = {-1.333333333, -1.333333333}

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