(u+5)(u+5)=2u^2+3u+31

Solution for (u+5)(u+5)=2u^2+3u+31 equation:

Simplifying
(u + 5)(u + 5) = 2u2 + 3u + 31

Reorder the terms:
(5 + u)(u + 5) = 2u2 + 3u + 31

Reorder the terms:
(5 + u)(5 + u) = 2u2 + 3u + 31

Multiply (5 + u) * (5 + u)
(5(5 + u) + u(5 + u)) = 2u2 + 3u + 31
((5 * 5 + u * 5) + u(5 + u)) = 2u2 + 3u + 31
((25 + 5u) + u(5 + u)) = 2u2 + 3u + 31
(25 + 5u + (5 * u + u * u)) = 2u2 + 3u + 31
(25 + 5u + (5u + u2)) = 2u2 + 3u + 31

Combine like terms: 5u + 5u = 10u
(25 + 10u + u2) = 2u2 + 3u + 31

Reorder the terms:
25 + 10u + u2 = 31 + 3u + 2u2

Solving
25 + 10u + u2 = 31 + 3u + 2u2

Solving for variable 'u'.

Reorder the terms:
25 + -31 + 10u + -3u + u2 + -2u2 = 31 + 3u + 2u2 + -31 + -3u + -2u2

Combine like terms: 25 + -31 = -6
-6 + 10u + -3u + u2 + -2u2 = 31 + 3u + 2u2 + -31 + -3u + -2u2

Combine like terms: 10u + -3u = 7u
-6 + 7u + u2 + -2u2 = 31 + 3u + 2u2 + -31 + -3u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-6 + 7u + -1u2 = 31 + 3u + 2u2 + -31 + -3u + -2u2

Reorder the terms:
-6 + 7u + -1u2 = 31 + -31 + 3u + -3u + 2u2 + -2u2

Combine like terms: 31 + -31 = 0
-6 + 7u + -1u2 = 0 + 3u + -3u + 2u2 + -2u2
-6 + 7u + -1u2 = 3u + -3u + 2u2 + -2u2

Combine like terms: 3u + -3u = 0
-6 + 7u + -1u2 = 0 + 2u2 + -2u2
-6 + 7u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-6 + 7u + -1u2 = 0

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

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 '(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
Solution
u = {6, 1}