(5q+9)(2q+2)+(5q+9)(q-2)=

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Solution for (5q+9)(2q+2)+(5q+9)(q-2)= equation: 


Simplifying
(5q + 9)(2q + 2) + (5q + 9)(q + -2) = 0

Reorder the terms:
(9 + 5q)(2q + 2) + (5q + 9)(q + -2) = 0

Reorder the terms:
(9 + 5q)(2 + 2q) + (5q + 9)(q + -2) = 0

Multiply (9 + 5q) * (2 + 2q)
(9(2 + 2q) + 5q * (2 + 2q)) + (5q + 9)(q + -2) = 0
((2 * 9 + 2q * 9) + 5q * (2 + 2q)) + (5q + 9)(q + -2) = 0
((18 + 18q) + 5q * (2 + 2q)) + (5q + 9)(q + -2) = 0
(18 + 18q + (2 * 5q + 2q * 5q)) + (5q + 9)(q + -2) = 0
(18 + 18q + (10q + 10q2)) + (5q + 9)(q + -2) = 0

Combine like terms: 18q + 10q = 28q
(18 + 28q + 10q2) + (5q + 9)(q + -2) = 0

Reorder the terms:
18 + 28q + 10q2 + (9 + 5q)(q + -2) = 0

Reorder the terms:
18 + 28q + 10q2 + (9 + 5q)(-2 + q) = 0

Multiply (9 + 5q) * (-2 + q)
18 + 28q + 10q2 + (9(-2 + q) + 5q * (-2 + q)) = 0
18 + 28q + 10q2 + ((-2 * 9 + q * 9) + 5q * (-2 + q)) = 0
18 + 28q + 10q2 + ((-18 + 9q) + 5q * (-2 + q)) = 0
18 + 28q + 10q2 + (-18 + 9q + (-2 * 5q + q * 5q)) = 0
18 + 28q + 10q2 + (-18 + 9q + (-10q + 5q2)) = 0

Combine like terms: 9q + -10q = -1q
18 + 28q + 10q2 + (-18 + -1q + 5q2) = 0

Reorder the terms:
18 + -18 + 28q + -1q + 10q2 + 5q2 = 0

Combine like terms: 18 + -18 = 0
0 + 28q + -1q + 10q2 + 5q2 = 0
28q + -1q + 10q2 + 5q2 = 0

Combine like terms: 28q + -1q = 27q
27q + 10q2 + 5q2 = 0

Combine like terms: 10q2 + 5q2 = 15q2
27q + 15q2 = 0

Solving
27q + 15q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3q'.
3q(9 + 5q) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0

Subproblem 2
Set the factor '(9 + 5q)' equal to zero and attempt to solve:

Simplifying
9 + 5q = 0

Solving
9 + 5q = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5q = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5q = 0 + -9
5q = 0 + -9

Combine like terms: 0 + -9 = -9
5q = -9

Divide each side by '5'.
q = -1.8

Simplifying
q = -1.8
Solution
q = {0, -1.8}

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