(u+7)(u+7)=2u^2+16u+25

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Solution for (u+7)(u+7)=2u^2+16u+25 equation: 


Simplifying
(u + 7)(u + 7) = 2u2 + 16u + 25

Reorder the terms:
(7 + u)(u + 7) = 2u2 + 16u + 25

Reorder the terms:
(7 + u)(7 + u) = 2u2 + 16u + 25

Multiply (7 + u) * (7 + u)
(7(7 + u) + u(7 + u)) = 2u2 + 16u + 25
((7 * 7 + u * 7) + u(7 + u)) = 2u2 + 16u + 25
((49 + 7u) + u(7 + u)) = 2u2 + 16u + 25
(49 + 7u + (7 * u + u * u)) = 2u2 + 16u + 25
(49 + 7u + (7u + u2)) = 2u2 + 16u + 25

Combine like terms: 7u + 7u = 14u
(49 + 14u + u2) = 2u2 + 16u + 25

Reorder the terms:
49 + 14u + u2 = 25 + 16u + 2u2

Solving
49 + 14u + u2 = 25 + 16u + 2u2

Solving for variable 'u'.

Reorder the terms:
49 + -25 + 14u + -16u + u2 + -2u2 = 25 + 16u + 2u2 + -25 + -16u + -2u2

Combine like terms: 49 + -25 = 24
24 + 14u + -16u + u2 + -2u2 = 25 + 16u + 2u2 + -25 + -16u + -2u2

Combine like terms: 14u + -16u = -2u
24 + -2u + u2 + -2u2 = 25 + 16u + 2u2 + -25 + -16u + -2u2

Combine like terms: u2 + -2u2 = -1u2
24 + -2u + -1u2 = 25 + 16u + 2u2 + -25 + -16u + -2u2

Reorder the terms:
24 + -2u + -1u2 = 25 + -25 + 16u + -16u + 2u2 + -2u2

Combine like terms: 25 + -25 = 0
24 + -2u + -1u2 = 0 + 16u + -16u + 2u2 + -2u2
24 + -2u + -1u2 = 16u + -16u + 2u2 + -2u2

Combine like terms: 16u + -16u = 0
24 + -2u + -1u2 = 0 + 2u2 + -2u2
24 + -2u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
24 + -2u + -1u2 = 0

Factor a trinomial.
(4 + -1u)(6 + u) = 0


Subproblem 1
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 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 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4

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 = {4, -6}

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