(2+3q)(4+3q)=80

Solution for (2+3q)(4+3q)=80 equation:

Simplifying
(2 + 3q)(4 + 3q) = 80

Multiply (2 + 3q) * (4 + 3q)
(2(4 + 3q) + 3q * (4 + 3q)) = 80
((4 * 2 + 3q * 2) + 3q * (4 + 3q)) = 80
((8 + 6q) + 3q * (4 + 3q)) = 80
(8 + 6q + (4 * 3q + 3q * 3q)) = 80
(8 + 6q + (12q + 9q2)) = 80

Combine like terms: 6q + 12q = 18q
(8 + 18q + 9q2) = 80

Solving
8 + 18q + 9q2 = 80

Solving for variable 'q'.

Reorder the terms:
8 + -80 + 18q + 9q2 = 80 + -80

Combine like terms: 8 + -80 = -72
-72 + 18q + 9q2 = 80 + -80

Combine like terms: 80 + -80 = 0
-72 + 18q + 9q2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-8 + 2q + q2) = 0

Factor a trinomial.
9((-4 + -1q)(2 + -1q)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-4 + -1q)' equal to zero and attempt to solve:

Simplifying
-4 + -1q = 0

Solving
-4 + -1q = 0

Move all terms containing q to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1q = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1q = 0 + 4
-1q = 0 + 4

Combine like terms: 0 + 4 = 4
-1q = 4

Divide each side by '-1'.
q = -4

Simplifying
q = -4
Subproblem 2
Set the factor '(2 + -1q)' equal to zero and attempt to solve:

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

Move all terms containing q to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Solution
q = {-4, 2}