(u+4)(u+4)=2u^2+17u+34

Solution for (u+4)(u+4)=2u^2+17u+34 equation:

Simplifying
(u + 4)(u + 4) = 2u2 + 17u + 34

Reorder the terms:
(4 + u)(u + 4) = 2u2 + 17u + 34

Reorder the terms:
(4 + u)(4 + u) = 2u2 + 17u + 34

Multiply (4 + u) * (4 + u)
(4(4 + u) + u(4 + u)) = 2u2 + 17u + 34
((4 * 4 + u * 4) + u(4 + u)) = 2u2 + 17u + 34
((16 + 4u) + u(4 + u)) = 2u2 + 17u + 34
(16 + 4u + (4 * u + u * u)) = 2u2 + 17u + 34
(16 + 4u + (4u + u2)) = 2u2 + 17u + 34

Combine like terms: 4u + 4u = 8u
(16 + 8u + u2) = 2u2 + 17u + 34

Reorder the terms:
16 + 8u + u2 = 34 + 17u + 2u2

Solving
16 + 8u + u2 = 34 + 17u + 2u2

Solving for variable 'u'.

Reorder the terms:
16 + -34 + 8u + -17u + u2 + -2u2 = 34 + 17u + 2u2 + -34 + -17u + -2u2

Combine like terms: 16 + -34 = -18
-18 + 8u + -17u + u2 + -2u2 = 34 + 17u + 2u2 + -34 + -17u + -2u2

Combine like terms: 8u + -17u = -9u
-18 + -9u + u2 + -2u2 = 34 + 17u + 2u2 + -34 + -17u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-18 + -9u + -1u2 = 34 + 17u + 2u2 + -34 + -17u + -2u2

Reorder the terms:
-18 + -9u + -1u2 = 34 + -34 + 17u + -17u + 2u2 + -2u2

Combine like terms: 34 + -34 = 0
-18 + -9u + -1u2 = 0 + 17u + -17u + 2u2 + -2u2
-18 + -9u + -1u2 = 17u + -17u + 2u2 + -2u2

Combine like terms: 17u + -17u = 0
-18 + -9u + -1u2 = 0 + 2u2 + -2u2
-18 + -9u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-18 + -9u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 9u + u2) = 0

Factor a trinomial.
-1((6 + u)(3 + u)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 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 + u = 0 + -6

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

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

Simplifying
u = -6
Subproblem 2
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 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 + u = 0 + -3

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

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

Simplifying
u = -3
Solution
u = {-6, -3}