8y^2-4y+12=0

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Solution for 8y^2-4y+12=0 equation: 


Simplifying
8y2 + -4y + 12 = 0

Reorder the terms:
12 + -4y + 8y2 = 0

Solving
12 + -4y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -1y + 2y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + -1y + 2y2)' equal to zero and attempt to solve:

Simplifying
3 + -1y + 2y2 = 0

Solving
3 + -1y + 2y2 = 0

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

Divide each side by '2'.
1.5 + -0.5y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5y + y2 = 0 + -1.5
-0.5y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5y + y2 = -1.5

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = -1.5 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = -1.5 + 0.0625

Combine like terms: -1.5 + 0.0625 = -1.4375
0.0625 + -0.5y + y2 = -1.4375

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = -1.4375

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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