(u+3)(u+3)=2u^2+15u+29

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Solution for (u+3)(u+3)=2u^2+15u+29 equation: 


Simplifying
(u + 3)(u + 3) = 2u2 + 15u + 29

Reorder the terms:
(3 + u)(u + 3) = 2u2 + 15u + 29

Reorder the terms:
(3 + u)(3 + u) = 2u2 + 15u + 29

Multiply (3 + u) * (3 + u)
(3(3 + u) + u(3 + u)) = 2u2 + 15u + 29
((3 * 3 + u * 3) + u(3 + u)) = 2u2 + 15u + 29
((9 + 3u) + u(3 + u)) = 2u2 + 15u + 29
(9 + 3u + (3 * u + u * u)) = 2u2 + 15u + 29
(9 + 3u + (3u + u2)) = 2u2 + 15u + 29

Combine like terms: 3u + 3u = 6u
(9 + 6u + u2) = 2u2 + 15u + 29

Reorder the terms:
9 + 6u + u2 = 29 + 15u + 2u2

Solving
9 + 6u + u2 = 29 + 15u + 2u2

Solving for variable 'u'.

Reorder the terms:
9 + -29 + 6u + -15u + u2 + -2u2 = 29 + 15u + 2u2 + -29 + -15u + -2u2

Combine like terms: 9 + -29 = -20
-20 + 6u + -15u + u2 + -2u2 = 29 + 15u + 2u2 + -29 + -15u + -2u2

Combine like terms: 6u + -15u = -9u
-20 + -9u + u2 + -2u2 = 29 + 15u + 2u2 + -29 + -15u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-20 + -9u + -1u2 = 29 + 15u + 2u2 + -29 + -15u + -2u2

Reorder the terms:
-20 + -9u + -1u2 = 29 + -29 + 15u + -15u + 2u2 + -2u2

Combine like terms: 29 + -29 = 0
-20 + -9u + -1u2 = 0 + 15u + -15u + 2u2 + -2u2
-20 + -9u + -1u2 = 15u + -15u + 2u2 + -2u2

Combine like terms: 15u + -15u = 0
-20 + -9u + -1u2 = 0 + 2u2 + -2u2
-20 + -9u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-20 + -9u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 9u + u2) = 0

Factor a trinomial.
-1((5 + u)(4 + 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 '(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 = {-5, -4}

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