u^2+4u-5=u^2+2u-15+u^2-4u+3

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Solution for u^2+4u-5=u^2+2u-15+u^2-4u+3 equation: 


Simplifying
u2 + 4u + -5 = u2 + 2u + -15 + u2 + -4u + 3

Reorder the terms:
-5 + 4u + u2 = u2 + 2u + -15 + u2 + -4u + 3

Reorder the terms:
-5 + 4u + u2 = -15 + 3 + 2u + -4u + u2 + u2

Combine like terms: -15 + 3 = -12
-5 + 4u + u2 = -12 + 2u + -4u + u2 + u2

Combine like terms: 2u + -4u = -2u
-5 + 4u + u2 = -12 + -2u + u2 + u2

Combine like terms: u2 + u2 = 2u2
-5 + 4u + u2 = -12 + -2u + 2u2

Solving
-5 + 4u + u2 = -12 + -2u + 2u2

Solving for variable 'u'.

Reorder the terms:
-5 + 12 + 4u + 2u + u2 + -2u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Combine like terms: -5 + 12 = 7
7 + 4u + 2u + u2 + -2u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Combine like terms: 4u + 2u = 6u
7 + 6u + u2 + -2u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Combine like terms: u2 + -2u2 = -1u2
7 + 6u + -1u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Reorder the terms:
7 + 6u + -1u2 = -12 + 12 + -2u + 2u + 2u2 + -2u2

Combine like terms: -12 + 12 = 0
7 + 6u + -1u2 = 0 + -2u + 2u + 2u2 + -2u2
7 + 6u + -1u2 = -2u + 2u + 2u2 + -2u2

Combine like terms: -2u + 2u = 0
7 + 6u + -1u2 = 0 + 2u2 + -2u2
7 + 6u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
7 + 6u + -1u2 = 0

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


Subproblem 1
Set the factor '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 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 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7

Subproblem 2
Set the factor '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

Solving
1 + u = 0

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

Add '-1' to each side of the equation.
1 + -1 + u = 0 + -1

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

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

Simplifying
u = -1
Solution
u = {7, -1}

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