(Q-45)(Q+39)=0

Solution for (Q-45)(Q+39)=0 equation:

Simplifying
(Q + -45)(Q + 39) = 0

Reorder the terms:
(-45 + Q)(Q + 39) = 0

Reorder the terms:
(-45 + Q)(39 + Q) = 0

Multiply (-45 + Q) * (39 + Q)
(-45(39 + Q) + Q(39 + Q)) = 0
((39 * -45 + Q * -45) + Q(39 + Q)) = 0
((-1755 + -45Q) + Q(39 + Q)) = 0
(-1755 + -45Q + (39 * Q + Q * Q)) = 0
(-1755 + -45Q + (39Q + Q2)) = 0

Combine like terms: -45Q + 39Q = -6Q
(-1755 + -6Q + Q2) = 0

Solving
-1755 + -6Q + Q2 = 0

Solving for variable 'Q'.

Factor a trinomial.
(-39 + -1Q)(45 + -1Q) = 0

Subproblem 1
Set the factor '(-39 + -1Q)' equal to zero and attempt to solve:

Simplifying
-39 + -1Q = 0

Solving
-39 + -1Q = 0

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

Add '39' to each side of the equation.
-39 + 39 + -1Q = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -1Q = 0 + 39
-1Q = 0 + 39

Combine like terms: 0 + 39 = 39
-1Q = 39

Divide each side by '-1'.
Q = -39

Simplifying
Q = -39
Subproblem 2
Set the factor '(45 + -1Q)' equal to zero and attempt to solve:

Simplifying
45 + -1Q = 0

Solving
45 + -1Q = 0

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

Add '-45' to each side of the equation.
45 + -45 + -1Q = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1Q = 0 + -45
-1Q = 0 + -45

Combine like terms: 0 + -45 = -45
-1Q = -45

Divide each side by '-1'.
Q = 45

Simplifying
Q = 45
Solution
Q = {-39, 45}