(2+y)*(2+y)=100-y^2

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Solution for (2+y)*(2+y)=100-y^2 equation: 


Simplifying
(2 + y)(2 + y) = 100 + -1y2

Multiply (2 + y) * (2 + y)
(2(2 + y) + y(2 + y)) = 100 + -1y2
((2 * 2 + y * 2) + y(2 + y)) = 100 + -1y2
((4 + 2y) + y(2 + y)) = 100 + -1y2
(4 + 2y + (2 * y + y * y)) = 100 + -1y2
(4 + 2y + (2y + y2)) = 100 + -1y2

Combine like terms: 2y + 2y = 4y
(4 + 4y + y2) = 100 + -1y2

Solving
4 + 4y + y2 = 100 + -1y2

Solving for variable 'y'.

Reorder the terms:
4 + -100 + 4y + y2 + y2 = 100 + -1y2 + -100 + y2

Combine like terms: 4 + -100 = -96
-96 + 4y + y2 + y2 = 100 + -1y2 + -100 + y2

Combine like terms: y2 + y2 = 2y2
-96 + 4y + 2y2 = 100 + -1y2 + -100 + y2

Reorder the terms:
-96 + 4y + 2y2 = 100 + -100 + -1y2 + y2

Combine like terms: 100 + -100 = 0
-96 + 4y + 2y2 = 0 + -1y2 + y2
-96 + 4y + 2y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-96 + 4y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 2y + y2) = 0

Factor a trinomial.
2((-8 + -1y)(6 + -1y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8

Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-8, 6}

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