(u-1)2=(u+1)(u+3)+5

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Solution for (u-1)2=(u+1)(u+3)+5 equation: 


Simplifying
(u + -1) * 2 = (u + 1)(u + 3) + 5

Reorder the terms:
(-1 + u) * 2 = (u + 1)(u + 3) + 5

Reorder the terms for easier multiplication:
2(-1 + u) = (u + 1)(u + 3) + 5
(-1 * 2 + u * 2) = (u + 1)(u + 3) + 5
(-2 + 2u) = (u + 1)(u + 3) + 5

Reorder the terms:
-2 + 2u = (1 + u)(u + 3) + 5

Reorder the terms:
-2 + 2u = (1 + u)(3 + u) + 5

Multiply (1 + u) * (3 + u)
-2 + 2u = (1(3 + u) + u(3 + u)) + 5
-2 + 2u = ((3 * 1 + u * 1) + u(3 + u)) + 5
-2 + 2u = ((3 + 1u) + u(3 + u)) + 5
-2 + 2u = (3 + 1u + (3 * u + u * u)) + 5
-2 + 2u = (3 + 1u + (3u + u2)) + 5

Combine like terms: 1u + 3u = 4u
-2 + 2u = (3 + 4u + u2) + 5

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

Combine like terms: 3 + 5 = 8
-2 + 2u = 8 + 4u + u2

Solving
-2 + 2u = 8 + 4u + u2

Solving for variable 'u'.

Reorder the terms:
-2 + -8 + 2u + -4u + -1u2 = 8 + 4u + u2 + -8 + -4u + -1u2

Combine like terms: -2 + -8 = -10
-10 + 2u + -4u + -1u2 = 8 + 4u + u2 + -8 + -4u + -1u2

Combine like terms: 2u + -4u = -2u
-10 + -2u + -1u2 = 8 + 4u + u2 + -8 + -4u + -1u2

Reorder the terms:
-10 + -2u + -1u2 = 8 + -8 + 4u + -4u + u2 + -1u2

Combine like terms: 8 + -8 = 0
-10 + -2u + -1u2 = 0 + 4u + -4u + u2 + -1u2
-10 + -2u + -1u2 = 4u + -4u + u2 + -1u2

Combine like terms: 4u + -4u = 0
-10 + -2u + -1u2 = 0 + u2 + -1u2
-10 + -2u + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-10 + -2u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 2u + u2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 2u + u2)' equal to zero and attempt to solve:

Simplifying
10 + 2u + u2 = 0

Solving
10 + 2u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 2u + -10 + u2 = 0 + -10

Reorder the terms:
10 + -10 + 2u + u2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 2u + u2 = 0 + -10
2u + u2 = 0 + -10

Combine like terms: 0 + -10 = -10
2u + u2 = -10

The u term is 2u.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2u + 1 + u2 = -10 + 1

Reorder the terms:
1 + 2u + u2 = -10 + 1

Combine like terms: -10 + 1 = -9
1 + 2u + u2 = -9

Factor a perfect square on the left side:
(u + 1)(u + 1) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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