u^2+9=2u^2+15u+23

Solution for u^2+9=2u^2+15u+23 equation:

Simplifying
u2 + 9 = 2u2 + 15u + 23

Reorder the terms:
9 + u2 = 2u2 + 15u + 23

Reorder the terms:
9 + u2 = 23 + 15u + 2u2

Solving
9 + u2 = 23 + 15u + 2u2

Solving for variable 'u'.

Reorder the terms:
9 + -23 + -15u + u2 + -2u2 = 23 + 15u + 2u2 + -23 + -15u + -2u2

Combine like terms: 9 + -23 = -14
-14 + -15u + u2 + -2u2 = 23 + 15u + 2u2 + -23 + -15u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-14 + -15u + -1u2 = 23 + 15u + 2u2 + -23 + -15u + -2u2

Reorder the terms:
-14 + -15u + -1u2 = 23 + -23 + 15u + -15u + 2u2 + -2u2

Combine like terms: 23 + -23 = 0
-14 + -15u + -1u2 = 0 + 15u + -15u + 2u2 + -2u2
-14 + -15u + -1u2 = 15u + -15u + 2u2 + -2u2

Combine like terms: 15u + -15u = 0
-14 + -15u + -1u2 = 0 + 2u2 + -2u2
-14 + -15u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-14 + -15u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 15u + u2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(14 + u)' equal to zero and attempt to solve:

Simplifying
14 + u = 0

Solving
14 + u = 0

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

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

Combine like terms: 14 + -14 = 0
0 + u = 0 + -14
u = 0 + -14

Combine like terms: 0 + -14 = -14
u = -14

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

Simplifying
1 + u = 0

Solving
1 + u = 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 + u = 0 + -1

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

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

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