2q(q-13)=28

Solution for 2q(q-13)=28 equation:

Simplifying
2q(q + -13) = 28

Reorder the terms:
2q(-13 + q) = 28
(-13 * 2q + q * 2q) = 28
(-26q + 2q2) = 28

Solving
-26q + 2q2 = 28

Solving for variable 'q'.

Reorder the terms:
-28 + -26q + 2q2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + -26q + 2q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -13q + q2) = 0

Factor a trinomial.
2((-1 + -1q)(14 + -1q)) = 0

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

Simplifying
-1 + -1q = 0

Solving
-1 + -1q = 0

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

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

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

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

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

Simplifying
q = -1
Subproblem 2
Set the factor '(14 + -1q)' equal to zero and attempt to solve:

Simplifying
14 + -1q = 0

Solving
14 + -1q = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1q = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1q = 0 + -14
-1q = 0 + -14

Combine like terms: 0 + -14 = -14
-1q = -14

Divide each side by '-1'.
q = 14

Simplifying
q = 14
Solution
q = {-1, 14}