(q+8)(4q-5)=0

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Solution for (q+8)(4q-5)=0 equation: 


Simplifying
(q + 8)(4q + -5) = 0

Reorder the terms:
(8 + q)(4q + -5) = 0

Reorder the terms:
(8 + q)(-5 + 4q) = 0

Multiply (8 + q) * (-5 + 4q)
(8(-5 + 4q) + q(-5 + 4q)) = 0
((-5 * 8 + 4q * 8) + q(-5 + 4q)) = 0
((-40 + 32q) + q(-5 + 4q)) = 0
(-40 + 32q + (-5 * q + 4q * q)) = 0
(-40 + 32q + (-5q + 4q2)) = 0

Combine like terms: 32q + -5q = 27q
(-40 + 27q + 4q2) = 0

Solving
-40 + 27q + 4q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-8 + -1q)(5 + -4q) = 0


Subproblem 1
Set the factor '(-8 + -1q)' equal to zero and attempt to solve:

Simplifying
-8 + -1q = 0

Solving
-8 + -1q = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1q = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1q = 0 + 8
-1q = 0 + 8

Combine like terms: 0 + 8 = 8
-1q = 8

Divide each side by '-1'.
q = -8

Simplifying
q = -8

Subproblem 2
Set the factor '(5 + -4q)' equal to zero and attempt to solve:

Simplifying
5 + -4q = 0

Solving
5 + -4q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4q = 0 + -5
-4q = 0 + -5

Combine like terms: 0 + -5 = -5
-4q = -5

Divide each side by '-4'.
q = 1.25

Simplifying
q = 1.25
Solution
q = {-8, 1.25}

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