10(2y+2)y=2(8y-8)

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


Simplifying
10(2y + 2) * y = 2(8y + -8)

Reorder the terms:
10(2 + 2y) * y = 2(8y + -8)

Reorder the terms for easier multiplication:
10y(2 + 2y) = 2(8y + -8)
(2 * 10y + 2y * 10y) = 2(8y + -8)
(20y + 20y2) = 2(8y + -8)

Reorder the terms:
20y + 20y2 = 2(-8 + 8y)
20y + 20y2 = (-8 * 2 + 8y * 2)
20y + 20y2 = (-16 + 16y)

Solving
20y + 20y2 = -16 + 16y

Solving for variable 'y'.

Reorder the terms:
16 + 20y + -16y + 20y2 = -16 + 16y + 16 + -16y

Combine like terms: 20y + -16y = 4y
16 + 4y + 20y2 = -16 + 16y + 16 + -16y

Reorder the terms:
16 + 4y + 20y2 = -16 + 16 + 16y + -16y

Combine like terms: -16 + 16 = 0
16 + 4y + 20y2 = 0 + 16y + -16y
16 + 4y + 20y2 = 16y + -16y

Combine like terms: 16y + -16y = 0
16 + 4y + 20y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + y + 5y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + y + 5y2)' equal to zero and attempt to solve:

Simplifying
4 + y + 5y2 = 0

Solving
4 + y + 5y2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.8 + 0.2y + y2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + 0.2y + -0.8 + y2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + 0.2y + y2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + 0.2y + y2 = 0 + -0.8
0.2y + y2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
0.2y + y2 = -0.8

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2y + 0.25 + y2 = -0.8 + 0.25

Reorder the terms:
0.25 + 0.2y + y2 = -0.8 + 0.25

Combine like terms: -0.8 + 0.25 = -0.55
0.25 + 0.2y + y2 = -0.55

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -0.55

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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