8(y+2)+4y=10y-2y^2-4

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Solution for 8(y+2)+4y=10y-2y^2-4 equation: 


Simplifying
8(y + 2) + 4y = 10y + -2y2 + -4

Reorder the terms:
8(2 + y) + 4y = 10y + -2y2 + -4
(2 * 8 + y * 8) + 4y = 10y + -2y2 + -4
(16 + 8y) + 4y = 10y + -2y2 + -4

Combine like terms: 8y + 4y = 12y
16 + 12y = 10y + -2y2 + -4

Reorder the terms:
16 + 12y = -4 + 10y + -2y2

Solving
16 + 12y = -4 + 10y + -2y2

Solving for variable 'y'.

Reorder the terms:
16 + 4 + 12y + -10y + 2y2 = -4 + 10y + -2y2 + 4 + -10y + 2y2

Combine like terms: 16 + 4 = 20
20 + 12y + -10y + 2y2 = -4 + 10y + -2y2 + 4 + -10y + 2y2

Combine like terms: 12y + -10y = 2y
20 + 2y + 2y2 = -4 + 10y + -2y2 + 4 + -10y + 2y2

Reorder the terms:
20 + 2y + 2y2 = -4 + 4 + 10y + -10y + -2y2 + 2y2

Combine like terms: -4 + 4 = 0
20 + 2y + 2y2 = 0 + 10y + -10y + -2y2 + 2y2
20 + 2y + 2y2 = 10y + -10y + -2y2 + 2y2

Combine like terms: 10y + -10y = 0
20 + 2y + 2y2 = 0 + -2y2 + 2y2
20 + 2y + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
20 + 2y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + y + y2)' equal to zero and attempt to solve:

Simplifying
10 + y + y2 = 0

Solving
10 + y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + y + y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y + y2 = 0 + -10
y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
y + y2 = -10

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.
y + 0.25 + y2 = -10 + 0.25

Reorder the terms:
0.25 + y + y2 = -10 + 0.25

Combine like terms: -10 + 0.25 = -9.75
0.25 + y + y2 = -9.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -9.75

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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