q^2+q-35=21

Solution for q^2+q-35=21 equation:

Simplifying
q2 + q + -35 = 21

Reorder the terms:
-35 + q + q2 = 21

Solving
-35 + q + q2 = 21

Solving for variable 'q'.

Reorder the terms:
-35 + -21 + q + q2 = 21 + -21

Combine like terms: -35 + -21 = -56
-56 + q + q2 = 21 + -21

Combine like terms: 21 + -21 = 0
-56 + q + q2 = 0

Factor a trinomial.
(-8 + -1q)(7 + -1q) = 0

Subproblem 1
Set the factor '(-8 + -1q)' equal to zero and attempt to solve:

Simplifying
-8 + -1q = 0

Solving
-8 + -1q = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1q = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1q = 0 + 8
-1q = 0 + 8

Combine like terms: 0 + 8 = 8
-1q = 8

Divide each side by '-1'.
q = -8

Simplifying
q = -8
Subproblem 2
Set the factor '(7 + -1q)' equal to zero and attempt to solve:

Simplifying
7 + -1q = 0

Solving
7 + -1q = 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 + -1q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1q = 0 + -7
-1q = 0 + -7

Combine like terms: 0 + -7 = -7
-1q = -7

Divide each side by '-1'.
q = 7

Simplifying
q = 7
Solution
q = {-8, 7}