u^2+12u+36=2u^2+23u+64

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Solution for u^2+12u+36=2u^2+23u+64 equation:


Simplifying
u2 + 12u + 36 = 2u2 + 23u + 64

Reorder the terms:
36 + 12u + u2 = 2u2 + 23u + 64

Reorder the terms:
36 + 12u + u2 = 64 + 23u + 2u2

Solving
36 + 12u + u2 = 64 + 23u + 2u2

Solving for variable 'u'.

Reorder the terms:
36 + -64 + 12u + -23u + u2 + -2u2 = 64 + 23u + 2u2 + -64 + -23u + -2u2

Combine like terms: 36 + -64 = -28
-28 + 12u + -23u + u2 + -2u2 = 64 + 23u + 2u2 + -64 + -23u + -2u2

Combine like terms: 12u + -23u = -11u
-28 + -11u + u2 + -2u2 = 64 + 23u + 2u2 + -64 + -23u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-28 + -11u + -1u2 = 64 + 23u + 2u2 + -64 + -23u + -2u2

Reorder the terms:
-28 + -11u + -1u2 = 64 + -64 + 23u + -23u + 2u2 + -2u2

Combine like terms: 64 + -64 = 0
-28 + -11u + -1u2 = 0 + 23u + -23u + 2u2 + -2u2
-28 + -11u + -1u2 = 23u + -23u + 2u2 + -2u2

Combine like terms: 23u + -23u = 0
-28 + -11u + -1u2 = 0 + 2u2 + -2u2
-28 + -11u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-28 + -11u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 11u + u2) = 0

Factor a trinomial.
-1((7 + u)(4 + u)) = 0

Ignore the factor -1.

Subproblem 1

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

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 = {-7, -4}

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