Y^2=(-8-3Y)(-8-3Y)-64

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Solution for Y^2=(-8-3Y)(-8-3Y)-64 equation: 


Simplifying
Y2 = (-8 + -3Y)(-8 + -3Y) + -64

Multiply (-8 + -3Y) * (-8 + -3Y)
Y2 = (-8(-8 + -3Y) + -3Y * (-8 + -3Y)) + -64
Y2 = ((-8 * -8 + -3Y * -8) + -3Y * (-8 + -3Y)) + -64
Y2 = ((64 + 24Y) + -3Y * (-8 + -3Y)) + -64
Y2 = (64 + 24Y + (-8 * -3Y + -3Y * -3Y)) + -64
Y2 = (64 + 24Y + (24Y + 9Y2)) + -64

Combine like terms: 24Y + 24Y = 48Y
Y2 = (64 + 48Y + 9Y2) + -64

Reorder the terms:
Y2 = 64 + -64 + 48Y + 9Y2

Combine like terms: 64 + -64 = 0
Y2 = 0 + 48Y + 9Y2
Y2 = 48Y + 9Y2

Solving
Y2 = 48Y + 9Y2

Solving for variable 'Y'.

Reorder the terms:
-48Y + Y2 + -9Y2 = 48Y + 9Y2 + -48Y + -9Y2

Combine like terms: Y2 + -9Y2 = -8Y2
-48Y + -8Y2 = 48Y + 9Y2 + -48Y + -9Y2

Reorder the terms:
-48Y + -8Y2 = 48Y + -48Y + 9Y2 + -9Y2

Combine like terms: 48Y + -48Y = 0
-48Y + -8Y2 = 0 + 9Y2 + -9Y2
-48Y + -8Y2 = 9Y2 + -9Y2

Combine like terms: 9Y2 + -9Y2 = 0
-48Y + -8Y2 = 0

Factor out the Greatest Common Factor (GCF), '-8Y'.
-8Y(6 + Y) = 0

Ignore the factor -8.

Subproblem 1
Set the factor 'Y' equal to zero and attempt to solve:

Simplifying
Y = 0

Solving
Y = 0

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

Simplifying
Y = 0

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

Simplifying
6 + Y = 0

Solving
6 + Y = 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 + Y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + Y = 0 + -6
Y = 0 + -6

Combine like terms: 0 + -6 = -6
Y = -6

Simplifying
Y = -6
Solution
Y = {0, -6}

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