-9y^2+15y+6=24

Solution for -9y^2+15y+6=24 equation:

Simplifying
-9y2 + 15y + 6 = 24

Reorder the terms:
6 + 15y + -9y2 = 24

Solving
6 + 15y + -9y2 = 24

Solving for variable 'y'.

Reorder the terms:
6 + -24 + 15y + -9y2 = 24 + -24

Combine like terms: 6 + -24 = -18
-18 + 15y + -9y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-18 + 15y + -9y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 5y + -3y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 5y + -3y2)' equal to zero and attempt to solve:

Simplifying
-6 + 5y + -3y2 = 0

Solving
-6 + 5y + -3y2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
2 + -1.666666667y + y2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1.666666667y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -1.666666667y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1.666666667y + y2 = 0 + -2
-1.666666667y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1.666666667y + y2 = -2

The y term is -1.666666667y.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667y + 0.6944444447 + y2 = -2 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667y + y2 = -2 + 0.6944444447

Combine like terms: -2 + 0.6944444447 = -1.3055555553
0.6944444447 + -1.666666667y + y2 = -1.3055555553

Factor a perfect square on the left side:
(y + -0.8333333335)(y + -0.8333333335) = -1.3055555553

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.