(u-5)(u+6)=12

Solution for (u-5)(u+6)=12 equation:

Simplifying
(u + -5)(u + 6) = 12

Reorder the terms:
(-5 + u)(u + 6) = 12

Reorder the terms:
(-5 + u)(6 + u) = 12

Multiply (-5 + u) * (6 + u)
(-5(6 + u) + u(6 + u)) = 12
((6 * -5 + u * -5) + u(6 + u)) = 12
((-30 + -5u) + u(6 + u)) = 12
(-30 + -5u + (6 * u + u * u)) = 12
(-30 + -5u + (6u + u2)) = 12

Combine like terms: -5u + 6u = 1u
(-30 + 1u + u2) = 12

Solving
-30 + 1u + u2 = 12

Solving for variable 'u'.

Reorder the terms:
-30 + -12 + 1u + u2 = 12 + -12

Combine like terms: -30 + -12 = -42
-42 + 1u + u2 = 12 + -12

Combine like terms: 12 + -12 = 0
-42 + 1u + u2 = 0

Factor a trinomial.
(-7 + -1u)(6 + -1u) = 0

Subproblem 1
Set the factor '(-7 + -1u)' equal to zero and attempt to solve:

Simplifying
-7 + -1u = 0

Solving
-7 + -1u = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1u = 0 + 7

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

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

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

Simplifying
u = -7
Subproblem 2
Set the factor '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {-7, 6}