(u+7)(u+7)=2u^2+17u+21

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Solution for (u+7)(u+7)=2u^2+17u+21 equation: 


Simplifying
(u + 7)(u + 7) = 2u2 + 17u + 21

Reorder the terms:
(7 + u)(u + 7) = 2u2 + 17u + 21

Reorder the terms:
(7 + u)(7 + u) = 2u2 + 17u + 21

Multiply (7 + u) * (7 + u)
(7(7 + u) + u(7 + u)) = 2u2 + 17u + 21
((7 * 7 + u * 7) + u(7 + u)) = 2u2 + 17u + 21
((49 + 7u) + u(7 + u)) = 2u2 + 17u + 21
(49 + 7u + (7 * u + u * u)) = 2u2 + 17u + 21
(49 + 7u + (7u + u2)) = 2u2 + 17u + 21

Combine like terms: 7u + 7u = 14u
(49 + 14u + u2) = 2u2 + 17u + 21

Reorder the terms:
49 + 14u + u2 = 21 + 17u + 2u2

Solving
49 + 14u + u2 = 21 + 17u + 2u2

Solving for variable 'u'.

Reorder the terms:
49 + -21 + 14u + -17u + u2 + -2u2 = 21 + 17u + 2u2 + -21 + -17u + -2u2

Combine like terms: 49 + -21 = 28
28 + 14u + -17u + u2 + -2u2 = 21 + 17u + 2u2 + -21 + -17u + -2u2

Combine like terms: 14u + -17u = -3u
28 + -3u + u2 + -2u2 = 21 + 17u + 2u2 + -21 + -17u + -2u2

Combine like terms: u2 + -2u2 = -1u2
28 + -3u + -1u2 = 21 + 17u + 2u2 + -21 + -17u + -2u2

Reorder the terms:
28 + -3u + -1u2 = 21 + -21 + 17u + -17u + 2u2 + -2u2

Combine like terms: 21 + -21 = 0
28 + -3u + -1u2 = 0 + 17u + -17u + 2u2 + -2u2
28 + -3u + -1u2 = 17u + -17u + 2u2 + -2u2

Combine like terms: 17u + -17u = 0
28 + -3u + -1u2 = 0 + 2u2 + -2u2
28 + -3u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
28 + -3u + -1u2 = 0

Factor a trinomial.
(4 + -1u)(7 + 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 '(7 + u)' equal to zero and attempt to solve:

Simplifying
7 + u = 0

Solving
7 + u = 0

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

Add '-7' to each side of the equation.
7 + -7 + u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + u = 0 + -7
u = 0 + -7

Combine like terms: 0 + -7 = -7
u = -7

Simplifying
u = -7
Solution
u = {4, -7}

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