45500=q(q-80)+47000

Solution for 45500=q(q-80)+47000 equation:

Simplifying
45500 = q(q + -80) + 47000

Reorder the terms:
45500 = q(-80 + q) + 47000
45500 = (-80 * q + q * q) + 47000
45500 = (-80q + q2) + 47000

Reorder the terms:
45500 = 47000 + -80q + q2

Solving
45500 = 47000 + -80q + q2

Solving for variable 'q'.

Combine like terms: 45500 + -47000 = -1500
-1500 + 80q + -1q2 = 47000 + -80q + q2 + -47000 + 80q + -1q2

Reorder the terms:
-1500 + 80q + -1q2 = 47000 + -47000 + -80q + 80q + q2 + -1q2

Combine like terms: 47000 + -47000 = 0
-1500 + 80q + -1q2 = 0 + -80q + 80q + q2 + -1q2
-1500 + 80q + -1q2 = -80q + 80q + q2 + -1q2

Combine like terms: -80q + 80q = 0
-1500 + 80q + -1q2 = 0 + q2 + -1q2
-1500 + 80q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
-1500 + 80q + -1q2 = 0

Factor a trinomial.
(-50 + q)(30 + -1q) = 0

Subproblem 1
Set the factor '(-50 + q)' equal to zero and attempt to solve:

Simplifying
-50 + q = 0

Solving
-50 + q = 0

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

Add '50' to each side of the equation.
-50 + 50 + q = 0 + 50

Combine like terms: -50 + 50 = 0
0 + q = 0 + 50
q = 0 + 50

Combine like terms: 0 + 50 = 50
q = 50

Simplifying
q = 50
Subproblem 2
Set the factor '(30 + -1q)' equal to zero and attempt to solve:

Simplifying
30 + -1q = 0

Solving
30 + -1q = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1q = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1q = 0 + -30
-1q = 0 + -30

Combine like terms: 0 + -30 = -30
-1q = -30

Divide each side by '-1'.
q = 30

Simplifying
q = 30
Solution
q = {50, 30}