2q^2-11q=21

Solution for 2q^2-11q=21 equation:

Simplifying
2q2 + -11q = 21

Reorder the terms:
-11q + 2q2 = 21

Solving
-11q + 2q2 = 21

Solving for variable 'q'.

Reorder the terms:
-21 + -11q + 2q2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -11q + 2q2 = 0

Factor a trinomial.
(-3 + -2q)(7 + -1q) = 0

Subproblem 1
Set the factor '(-3 + -2q)' equal to zero and attempt to solve:

Simplifying
-3 + -2q = 0

Solving
-3 + -2q = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2q = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2q = 0 + 3
-2q = 0 + 3

Combine like terms: 0 + 3 = 3
-2q = 3

Divide each side by '-2'.
q = -1.5

Simplifying
q = -1.5
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 = {-1.5, 7}