6=42-5q-q^2

Solution for 6=42-5q-q^2 equation:

Simplifying
6 = 42 + -5q + -1q2

Solving
6 = 42 + -5q + -1q2

Solving for variable 'q'.

Combine like terms: 6 + -42 = -36
-36 + 5q + q2 = 42 + -5q + -1q2 + -42 + 5q + q2

Reorder the terms:
-36 + 5q + q2 = 42 + -42 + -5q + 5q + -1q2 + q2

Combine like terms: 42 + -42 = 0
-36 + 5q + q2 = 0 + -5q + 5q + -1q2 + q2
-36 + 5q + q2 = -5q + 5q + -1q2 + q2

Combine like terms: -5q + 5q = 0
-36 + 5q + q2 = 0 + -1q2 + q2
-36 + 5q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-36 + 5q + q2 = 0

Factor a trinomial.
(-9 + -1q)(4 + -1q) = 0

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

Simplifying
-9 + -1q = 0

Solving
-9 + -1q = 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 + -1q = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1q = 0 + 9
-1q = 0 + 9

Combine like terms: 0 + 9 = 9
-1q = 9

Divide each side by '-1'.
q = -9

Simplifying
q = -9
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 = {-9, 4}