12(5y+27)=4y(6-9y)

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Solution for 12(5y+27)=4y(6-9y) equation: 


Simplifying
12(5y + 27) = 4y(6 + -9y)

Reorder the terms:
12(27 + 5y) = 4y(6 + -9y)
(27 * 12 + 5y * 12) = 4y(6 + -9y)
(324 + 60y) = 4y(6 + -9y)
324 + 60y = (6 * 4y + -9y * 4y)
324 + 60y = (24y + -36y2)

Solving
324 + 60y = 24y + -36y2

Solving for variable 'y'.

Combine like terms: 60y + -24y = 36y
324 + 36y + 36y2 = 24y + -36y2 + -24y + 36y2

Reorder the terms:
324 + 36y + 36y2 = 24y + -24y + -36y2 + 36y2

Combine like terms: 24y + -24y = 0
324 + 36y + 36y2 = 0 + -36y2 + 36y2
324 + 36y + 36y2 = -36y2 + 36y2

Combine like terms: -36y2 + 36y2 = 0
324 + 36y + 36y2 = 0

Factor out the Greatest Common Factor (GCF), '36'.
36(9 + y + y2) = 0

Ignore the factor 36.

Subproblem 1
Set the factor '(9 + y + y2)' equal to zero and attempt to solve:

Simplifying
9 + y + y2 = 0

Solving
9 + y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + y + -9 + y2 = 0 + -9

Reorder the terms:
9 + -9 + y + y2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y + y2 = 0 + -9
y + y2 = 0 + -9

Combine like terms: 0 + -9 = -9
y + y2 = -9

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 = -9 + 0.25

Reorder the terms:
0.25 + y + y2 = -9 + 0.25

Combine like terms: -9 + 0.25 = -8.75
0.25 + y + y2 = -8.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -8.75

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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