(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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