(u-2)(u-2)=2u^2+2u+9

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Solution for (u-2)(u-2)=2u^2+2u+9 equation: 


Simplifying
(u + -2)(u + -2) = 2u2 + 2u + 9

Reorder the terms:
(-2 + u)(u + -2) = 2u2 + 2u + 9

Reorder the terms:
(-2 + u)(-2 + u) = 2u2 + 2u + 9

Multiply (-2 + u) * (-2 + u)
(-2(-2 + u) + u(-2 + u)) = 2u2 + 2u + 9
((-2 * -2 + u * -2) + u(-2 + u)) = 2u2 + 2u + 9
((4 + -2u) + u(-2 + u)) = 2u2 + 2u + 9
(4 + -2u + (-2 * u + u * u)) = 2u2 + 2u + 9
(4 + -2u + (-2u + u2)) = 2u2 + 2u + 9

Combine like terms: -2u + -2u = -4u
(4 + -4u + u2) = 2u2 + 2u + 9

Reorder the terms:
4 + -4u + u2 = 9 + 2u + 2u2

Solving
4 + -4u + u2 = 9 + 2u + 2u2

Solving for variable 'u'.

Reorder the terms:
4 + -9 + -4u + -2u + u2 + -2u2 = 9 + 2u + 2u2 + -9 + -2u + -2u2

Combine like terms: 4 + -9 = -5
-5 + -4u + -2u + u2 + -2u2 = 9 + 2u + 2u2 + -9 + -2u + -2u2

Combine like terms: -4u + -2u = -6u
-5 + -6u + u2 + -2u2 = 9 + 2u + 2u2 + -9 + -2u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-5 + -6u + -1u2 = 9 + 2u + 2u2 + -9 + -2u + -2u2

Reorder the terms:
-5 + -6u + -1u2 = 9 + -9 + 2u + -2u + 2u2 + -2u2

Combine like terms: 9 + -9 = 0
-5 + -6u + -1u2 = 0 + 2u + -2u + 2u2 + -2u2
-5 + -6u + -1u2 = 2u + -2u + 2u2 + -2u2

Combine like terms: 2u + -2u = 0
-5 + -6u + -1u2 = 0 + 2u2 + -2u2
-5 + -6u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-5 + -6u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 6u + u2) = 0

Factor a trinomial.
-1((5 + u)(1 + u)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + u)' equal to zero and attempt to solve:

Simplifying
5 + u = 0

Solving
5 + u = 0

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

Add '-5' to each side of the equation.
5 + -5 + u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + u = 0 + -5
u = 0 + -5

Combine like terms: 0 + -5 = -5
u = -5

Simplifying
u = -5

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 = {-5, -1}

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