6(y)-2(y)y=24

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Solution for 6(y)-2(y)y=24 equation: 


Simplifying
6(y) + -2(y) * y = 24

Multiply y * y
6y + -2y2 = 24

Solving
6y + -2y2 = 24

Solving for variable 'y'.

Reorder the terms:
-24 + 6y + -2y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 6y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 3y + -1y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 3y + -1y2)' equal to zero and attempt to solve:

Simplifying
-12 + 3y + -1y2 = 0

Solving
-12 + 3y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
12 + -3y + y2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -3y + -12 + y2 = 0 + -12

Reorder the terms:
12 + -12 + -3y + y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -3y + y2 = 0 + -12
-3y + y2 = 0 + -12

Combine like terms: 0 + -12 = -12
-3y + y2 = -12

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -12 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -12 + 2.25

Combine like terms: -12 + 2.25 = -9.75
2.25 + -3y + y2 = -9.75

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = -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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