2u^2-2u-12=u^2-9

Solution for 2u^2-2u-12=u^2-9 equation:

Simplifying
2u2 + -2u + -12 = u2 + -9

Reorder the terms:
-12 + -2u + 2u2 = u2 + -9

Reorder the terms:
-12 + -2u + 2u2 = -9 + u2

Solving
-12 + -2u + 2u2 = -9 + u2

Solving for variable 'u'.

Reorder the terms:
-12 + 9 + -2u + 2u2 + -1u2 = -9 + u2 + 9 + -1u2

Combine like terms: -12 + 9 = -3
-3 + -2u + 2u2 + -1u2 = -9 + u2 + 9 + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-3 + -2u + 1u2 = -9 + u2 + 9 + -1u2

Reorder the terms:
-3 + -2u + 1u2 = -9 + 9 + u2 + -1u2

Combine like terms: -9 + 9 = 0
-3 + -2u + 1u2 = 0 + u2 + -1u2
-3 + -2u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-3 + -2u + 1u2 = 0

Factor a trinomial.
(-1 + -1u)(3 + -1u) = 0

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

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

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

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

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

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

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {-1, 3}