(u-7)(u-7)=2u^2-6u+64

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Solution for (u-7)(u-7)=2u^2-6u+64 equation: 


Simplifying
(u + -7)(u + -7) = 2u2 + -6u + 64

Reorder the terms:
(-7 + u)(u + -7) = 2u2 + -6u + 64

Reorder the terms:
(-7 + u)(-7 + u) = 2u2 + -6u + 64

Multiply (-7 + u) * (-7 + u)
(-7(-7 + u) + u(-7 + u)) = 2u2 + -6u + 64
((-7 * -7 + u * -7) + u(-7 + u)) = 2u2 + -6u + 64
((49 + -7u) + u(-7 + u)) = 2u2 + -6u + 64
(49 + -7u + (-7 * u + u * u)) = 2u2 + -6u + 64
(49 + -7u + (-7u + u2)) = 2u2 + -6u + 64

Combine like terms: -7u + -7u = -14u
(49 + -14u + u2) = 2u2 + -6u + 64

Reorder the terms:
49 + -14u + u2 = 64 + -6u + 2u2

Solving
49 + -14u + u2 = 64 + -6u + 2u2

Solving for variable 'u'.

Reorder the terms:
49 + -64 + -14u + 6u + u2 + -2u2 = 64 + -6u + 2u2 + -64 + 6u + -2u2

Combine like terms: 49 + -64 = -15
-15 + -14u + 6u + u2 + -2u2 = 64 + -6u + 2u2 + -64 + 6u + -2u2

Combine like terms: -14u + 6u = -8u
-15 + -8u + u2 + -2u2 = 64 + -6u + 2u2 + -64 + 6u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-15 + -8u + -1u2 = 64 + -6u + 2u2 + -64 + 6u + -2u2

Reorder the terms:
-15 + -8u + -1u2 = 64 + -64 + -6u + 6u + 2u2 + -2u2

Combine like terms: 64 + -64 = 0
-15 + -8u + -1u2 = 0 + -6u + 6u + 2u2 + -2u2
-15 + -8u + -1u2 = -6u + 6u + 2u2 + -2u2

Combine like terms: -6u + 6u = 0
-15 + -8u + -1u2 = 0 + 2u2 + -2u2
-15 + -8u + -1u2 = 2u2 + -2u2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 8u + u2) = 0

Factor a trinomial.
-1((5 + u)(3 + 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 '(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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