(u-6)(u-6)=2u^2-10u+28

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Solution for (u-6)(u-6)=2u^2-10u+28 equation: 


Simplifying
(u + -6)(u + -6) = 2u2 + -10u + 28

Reorder the terms:
(-6 + u)(u + -6) = 2u2 + -10u + 28

Reorder the terms:
(-6 + u)(-6 + u) = 2u2 + -10u + 28

Multiply (-6 + u) * (-6 + u)
(-6(-6 + u) + u(-6 + u)) = 2u2 + -10u + 28
((-6 * -6 + u * -6) + u(-6 + u)) = 2u2 + -10u + 28
((36 + -6u) + u(-6 + u)) = 2u2 + -10u + 28
(36 + -6u + (-6 * u + u * u)) = 2u2 + -10u + 28
(36 + -6u + (-6u + u2)) = 2u2 + -10u + 28

Combine like terms: -6u + -6u = -12u
(36 + -12u + u2) = 2u2 + -10u + 28

Reorder the terms:
36 + -12u + u2 = 28 + -10u + 2u2

Solving
36 + -12u + u2 = 28 + -10u + 2u2

Solving for variable 'u'.

Reorder the terms:
36 + -28 + -12u + 10u + u2 + -2u2 = 28 + -10u + 2u2 + -28 + 10u + -2u2

Combine like terms: 36 + -28 = 8
8 + -12u + 10u + u2 + -2u2 = 28 + -10u + 2u2 + -28 + 10u + -2u2

Combine like terms: -12u + 10u = -2u
8 + -2u + u2 + -2u2 = 28 + -10u + 2u2 + -28 + 10u + -2u2

Combine like terms: u2 + -2u2 = -1u2
8 + -2u + -1u2 = 28 + -10u + 2u2 + -28 + 10u + -2u2

Reorder the terms:
8 + -2u + -1u2 = 28 + -28 + -10u + 10u + 2u2 + -2u2

Combine like terms: 28 + -28 = 0
8 + -2u + -1u2 = 0 + -10u + 10u + 2u2 + -2u2
8 + -2u + -1u2 = -10u + 10u + 2u2 + -2u2

Combine like terms: -10u + 10u = 0
8 + -2u + -1u2 = 0 + 2u2 + -2u2
8 + -2u + -1u2 = 2u2 + -2u2

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

Factor a trinomial.
(2 + -1u)(4 + 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 '(4 + u)' equal to zero and attempt to solve:

Simplifying
4 + u = 0

Solving
4 + u = 0

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

Add '-4' to each side of the equation.
4 + -4 + u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + u = 0 + -4
u = 0 + -4

Combine like terms: 0 + -4 = -4
u = -4

Simplifying
u = -4
Solution
u = {2, -4}

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