2y^2-y+8=3y-8y-12

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Solution for 2y^2-y+8=3y-8y-12 equation: 


Simplifying
2y2 + -1y + 8 = 3y + -8y + -12

Reorder the terms:
8 + -1y + 2y2 = 3y + -8y + -12

Reorder the terms:
8 + -1y + 2y2 = -12 + 3y + -8y

Combine like terms: 3y + -8y = -5y
8 + -1y + 2y2 = -12 + -5y

Solving
8 + -1y + 2y2 = -12 + -5y

Solving for variable 'y'.

Reorder the terms:
8 + 12 + -1y + 5y + 2y2 = -12 + -5y + 12 + 5y

Combine like terms: 8 + 12 = 20
20 + -1y + 5y + 2y2 = -12 + -5y + 12 + 5y

Combine like terms: -1y + 5y = 4y
20 + 4y + 2y2 = -12 + -5y + 12 + 5y

Reorder the terms:
20 + 4y + 2y2 = -12 + 12 + -5y + 5y

Combine like terms: -12 + 12 = 0
20 + 4y + 2y2 = 0 + -5y + 5y
20 + 4y + 2y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
20 + 4y + 2y2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
10 + 2y + y2 = 0

Solving
10 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 2y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + 2y + y2 = 0 + -10

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

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

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -10 + 1

Reorder the terms:
1 + 2y + y2 = -10 + 1

Combine like terms: -10 + 1 = -9
1 + 2y + y2 = -9

Factor a perfect square on the left side:
(y + 1)(y + 1) = -9

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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