Y(Y-8)(16)+(Y+8)(Y-8)(2)=Y(10Y-8)

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Solution for Y(Y-8)(16)+(Y+8)(Y-8)(2)=Y(10Y-8) equation: 


Simplifying
Y(Y + -8)(16) + (Y + 8)(Y + -8)(2) = Y(10Y + -8)

Reorder the terms:
Y(-8 + Y)(16) + (Y + 8)(Y + -8)(2) = Y(10Y + -8)

Reorder the terms for easier multiplication:
16Y(-8 + Y) + (Y + 8)(Y + -8)(2) = Y(10Y + -8)
(-8 * 16Y + Y * 16Y) + (Y + 8)(Y + -8)(2) = Y(10Y + -8)
(-128Y + 16Y2) + (Y + 8)(Y + -8)(2) = Y(10Y + -8)

Reorder the terms:
-128Y + 16Y2 + (8 + Y)(Y + -8)(2) = Y(10Y + -8)

Reorder the terms:
-128Y + 16Y2 + (8 + Y)(-8 + Y)(2) = Y(10Y + -8)

Reorder the terms for easier multiplication:
-128Y + 16Y2 + 2(8 + Y)(-8 + Y) = Y(10Y + -8)

Multiply (8 + Y) * (-8 + Y)
-128Y + 16Y2 + 2(8(-8 + Y) + Y(-8 + Y)) = Y(10Y + -8)
-128Y + 16Y2 + 2((-8 * 8 + Y * 8) + Y(-8 + Y)) = Y(10Y + -8)
-128Y + 16Y2 + 2((-64 + 8Y) + Y(-8 + Y)) = Y(10Y + -8)
-128Y + 16Y2 + 2(-64 + 8Y + (-8 * Y + Y * Y)) = Y(10Y + -8)
-128Y + 16Y2 + 2(-64 + 8Y + (-8Y + Y2)) = Y(10Y + -8)

Combine like terms: 8Y + -8Y = 0
-128Y + 16Y2 + 2(-64 + 0 + Y2) = Y(10Y + -8)
-128Y + 16Y2 + 2(-64 + Y2) = Y(10Y + -8)
-128Y + 16Y2 + (-64 * 2 + Y2 * 2) = Y(10Y + -8)
-128Y + 16Y2 + (-128 + 2Y2) = Y(10Y + -8)

Reorder the terms:
-128 + -128Y + 16Y2 + 2Y2 = Y(10Y + -8)

Combine like terms: 16Y2 + 2Y2 = 18Y2
-128 + -128Y + 18Y2 = Y(10Y + -8)

Reorder the terms:
-128 + -128Y + 18Y2 = Y(-8 + 10Y)
-128 + -128Y + 18Y2 = (-8 * Y + 10Y * Y)
-128 + -128Y + 18Y2 = (-8Y + 10Y2)

Solving
-128 + -128Y + 18Y2 = -8Y + 10Y2

Solving for variable 'Y'.

Reorder the terms:
-128 + -128Y + 8Y + 18Y2 + -10Y2 = -8Y + 10Y2 + 8Y + -10Y2

Combine like terms: -128Y + 8Y = -120Y
-128 + -120Y + 18Y2 + -10Y2 = -8Y + 10Y2 + 8Y + -10Y2

Combine like terms: 18Y2 + -10Y2 = 8Y2
-128 + -120Y + 8Y2 = -8Y + 10Y2 + 8Y + -10Y2

Reorder the terms:
-128 + -120Y + 8Y2 = -8Y + 8Y + 10Y2 + -10Y2

Combine like terms: -8Y + 8Y = 0
-128 + -120Y + 8Y2 = 0 + 10Y2 + -10Y2
-128 + -120Y + 8Y2 = 10Y2 + -10Y2

Combine like terms: 10Y2 + -10Y2 = 0
-128 + -120Y + 8Y2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-16 + -15Y + Y2) = 0

Factor a trinomial.
8((-1 + -1Y)(16 + -1Y)) = 0

Ignore the factor 8.

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

Simplifying
-1 + -1Y = 0

Solving
-1 + -1Y = 0

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

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

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

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

Divide each side by '-1'.
Y = -1

Simplifying
Y = -1

Subproblem 2
Set the factor '(16 + -1Y)' equal to zero and attempt to solve:

Simplifying
16 + -1Y = 0

Solving
16 + -1Y = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1Y = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1Y = 0 + -16
-1Y = 0 + -16

Combine like terms: 0 + -16 = -16
-1Y = -16

Divide each side by '-1'.
Y = 16

Simplifying
Y = 16
Solution
Y = {-1, 16}

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