-5q^2+55q-140=0

Solution for -5q^2+55q-140=0 equation:

Simplifying
-5q2 + 55q + -140 = 0

Reorder the terms:
-140 + 55q + -5q2 = 0

Solving
-140 + 55q + -5q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + 11q + -1q2) = 0

Factor a trinomial.
5((-7 + q)(4 + -1q)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-7 + q)' equal to zero and attempt to solve:

Simplifying
-7 + q = 0

Solving
-7 + q = 0

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

Add '7' to each side of the equation.
-7 + 7 + q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + q = 0 + 7
q = 0 + 7

Combine like terms: 0 + 7 = 7
q = 7

Simplifying
q = 7
Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

Simplifying
q = 4
Solution
q = {7, 4}