(9q-10)(4q+9)=0

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Solution for (9q-10)(4q+9)=0 equation: 


Simplifying
(9q + -10)(4q + 9) = 0

Reorder the terms:
(-10 + 9q)(4q + 9) = 0

Reorder the terms:
(-10 + 9q)(9 + 4q) = 0

Multiply (-10 + 9q) * (9 + 4q)
(-10(9 + 4q) + 9q * (9 + 4q)) = 0
((9 * -10 + 4q * -10) + 9q * (9 + 4q)) = 0
((-90 + -40q) + 9q * (9 + 4q)) = 0
(-90 + -40q + (9 * 9q + 4q * 9q)) = 0
(-90 + -40q + (81q + 36q2)) = 0

Combine like terms: -40q + 81q = 41q
(-90 + 41q + 36q2) = 0

Solving
-90 + 41q + 36q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-9 + -4q)(10 + -9q) = 0


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

Simplifying
-9 + -4q = 0

Solving
-9 + -4q = 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 + -4q = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4q = 0 + 9
-4q = 0 + 9

Combine like terms: 0 + 9 = 9
-4q = 9

Divide each side by '-4'.
q = -2.25

Simplifying
q = -2.25

Subproblem 2
Set the factor '(10 + -9q)' equal to zero and attempt to solve:

Simplifying
10 + -9q = 0

Solving
10 + -9q = 0

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

Add '-10' to each side of the equation.
10 + -10 + -9q = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -9q = 0 + -10
-9q = 0 + -10

Combine like terms: 0 + -10 = -10
-9q = -10

Divide each side by '-9'.
q = 1.111111111

Simplifying
q = 1.111111111
Solution
q = {-2.25, 1.111111111}

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