2u^2+6u+16=(u-1)(u-1)

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Solution for 2u^2+6u+16=(u-1)(u-1) equation: 


Simplifying
2u2 + 6u + 16 = (u + -1)(u + -1)

Reorder the terms:
16 + 6u + 2u2 = (u + -1)(u + -1)

Reorder the terms:
16 + 6u + 2u2 = (-1 + u)(u + -1)

Reorder the terms:
16 + 6u + 2u2 = (-1 + u)(-1 + u)

Multiply (-1 + u) * (-1 + u)
16 + 6u + 2u2 = (-1(-1 + u) + u(-1 + u))
16 + 6u + 2u2 = ((-1 * -1 + u * -1) + u(-1 + u))
16 + 6u + 2u2 = ((1 + -1u) + u(-1 + u))
16 + 6u + 2u2 = (1 + -1u + (-1 * u + u * u))
16 + 6u + 2u2 = (1 + -1u + (-1u + u2))

Combine like terms: -1u + -1u = -2u
16 + 6u + 2u2 = (1 + -2u + u2)

Solving
16 + 6u + 2u2 = 1 + -2u + u2

Solving for variable 'u'.

Reorder the terms:
16 + -1 + 6u + 2u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: 16 + -1 = 15
15 + 6u + 2u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: 6u + 2u = 8u
15 + 8u + 2u2 + -1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
15 + 8u + 1u2 = 1 + -2u + u2 + -1 + 2u + -1u2

Reorder the terms:
15 + 8u + 1u2 = 1 + -1 + -2u + 2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
15 + 8u + 1u2 = 0 + -2u + 2u + u2 + -1u2
15 + 8u + 1u2 = -2u + 2u + u2 + -1u2

Combine like terms: -2u + 2u = 0
15 + 8u + 1u2 = 0 + u2 + -1u2
15 + 8u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
15 + 8u + 1u2 = 0

Factor a trinomial.
(5 + u)(3 + u) = 0


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 '(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 = {-5, -3}

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