(u+1)(u+1)=2u^2+6u-11

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Solution for (u+1)(u+1)=2u^2+6u-11 equation: 


Simplifying
(u + 1)(u + 1) = 2u2 + 6u + -11

Reorder the terms:
(1 + u)(u + 1) = 2u2 + 6u + -11

Reorder the terms:
(1 + u)(1 + u) = 2u2 + 6u + -11

Multiply (1 + u) * (1 + u)
(1(1 + u) + u(1 + u)) = 2u2 + 6u + -11
((1 * 1 + u * 1) + u(1 + u)) = 2u2 + 6u + -11
((1 + 1u) + u(1 + u)) = 2u2 + 6u + -11
(1 + 1u + (1 * u + u * u)) = 2u2 + 6u + -11
(1 + 1u + (1u + u2)) = 2u2 + 6u + -11

Combine like terms: 1u + 1u = 2u
(1 + 2u + u2) = 2u2 + 6u + -11

Reorder the terms:
1 + 2u + u2 = -11 + 6u + 2u2

Solving
1 + 2u + u2 = -11 + 6u + 2u2

Solving for variable 'u'.

Reorder the terms:
1 + 11 + 2u + -6u + u2 + -2u2 = -11 + 6u + 2u2 + 11 + -6u + -2u2

Combine like terms: 1 + 11 = 12
12 + 2u + -6u + u2 + -2u2 = -11 + 6u + 2u2 + 11 + -6u + -2u2

Combine like terms: 2u + -6u = -4u
12 + -4u + u2 + -2u2 = -11 + 6u + 2u2 + 11 + -6u + -2u2

Combine like terms: u2 + -2u2 = -1u2
12 + -4u + -1u2 = -11 + 6u + 2u2 + 11 + -6u + -2u2

Reorder the terms:
12 + -4u + -1u2 = -11 + 11 + 6u + -6u + 2u2 + -2u2

Combine like terms: -11 + 11 = 0
12 + -4u + -1u2 = 0 + 6u + -6u + 2u2 + -2u2
12 + -4u + -1u2 = 6u + -6u + 2u2 + -2u2

Combine like terms: 6u + -6u = 0
12 + -4u + -1u2 = 0 + 2u2 + -2u2
12 + -4u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
12 + -4u + -1u2 = 0

Factor a trinomial.
(2 + -1u)(6 + u) = 0


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

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

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

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

Divide each side by '-1'.
u = 2

Simplifying
u = 2

Subproblem 2
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
Solution
u = {2, -6}

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