(y-2)(3+2y)-y^2=y^2+5

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Solution for (y-2)(3+2y)-y^2=y^2+5 equation:


Simplifying
(y + -2)(3 + 2y) + -1y2 = y2 + 5

Reorder the terms:
(-2 + y)(3 + 2y) + -1y2 = y2 + 5

Multiply (-2 + y) * (3 + 2y)
(-2(3 + 2y) + y(3 + 2y)) + -1y2 = y2 + 5
((3 * -2 + 2y * -2) + y(3 + 2y)) + -1y2 = y2 + 5
((-6 + -4y) + y(3 + 2y)) + -1y2 = y2 + 5
(-6 + -4y + (3 * y + 2y * y)) + -1y2 = y2 + 5
(-6 + -4y + (3y + 2y2)) + -1y2 = y2 + 5

Combine like terms: -4y + 3y = -1y
(-6 + -1y + 2y2) + -1y2 = y2 + 5

Combine like terms: 2y2 + -1y2 = 1y2
-6 + -1y + 1y2 = y2 + 5

Reorder the terms:
-6 + -1y + 1y2 = 5 + y2

Solving
-6 + -1y + 1y2 = 5 + y2

Solving for variable 'y'.

Reorder the terms:
-6 + -5 + -1y + 1y2 + -1y2 = 5 + y2 + -5 + -1y2

Combine like terms: -6 + -5 = -11
-11 + -1y + 1y2 + -1y2 = 5 + y2 + -5 + -1y2

Combine like terms: 1y2 + -1y2 = 0
-11 + -1y + 0 = 5 + y2 + -5 + -1y2
-11 + -1y = 5 + y2 + -5 + -1y2

Reorder the terms:
-11 + -1y = 5 + -5 + y2 + -1y2

Combine like terms: 5 + -5 = 0
-11 + -1y = 0 + y2 + -1y2
-11 + -1y = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-11 + -1y = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(11 + y)' equal to zero and attempt to solve:

Simplifying
11 + y = 0

Solving
11 + y = 0

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

Add '-11' to each side of the equation.
11 + -11 + y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + y = 0 + -11
y = 0 + -11

Combine like terms: 0 + -11 = -11
y = -11

Simplifying
y = -11
Solution
y = {-11}

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