2y-15=(3y+4y^2)

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Solution for 2y-15=(3y+4y^2) equation: 


Simplifying
2y + -15 = (3y + 4y2)

Reorder the terms:
-15 + 2y = (3y + 4y2)

Remove parenthesis around (3y + 4y2)
-15 + 2y = 3y + 4y2

Solving
-15 + 2y = 3y + 4y2

Solving for variable 'y'.

Combine like terms: 2y + -3y = -1y
-15 + -1y + -4y2 = 3y + 4y2 + -3y + -4y2

Reorder the terms:
-15 + -1y + -4y2 = 3y + -3y + 4y2 + -4y2

Combine like terms: 3y + -3y = 0
-15 + -1y + -4y2 = 0 + 4y2 + -4y2
-15 + -1y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-15 + -1y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + y + 4y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(15 + y + 4y2)' equal to zero and attempt to solve:

Simplifying
15 + y + 4y2 = 0

Solving
15 + y + 4y2 = 0

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

Divide each side by '4'.
3.75 + 0.25y + y2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 0.25y + -3.75 + y2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 0.25y + y2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 0.25y + y2 = 0 + -3.75
0.25y + y2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
0.25y + y2 = -3.75

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.
0.25y + 0.25 + y2 = -3.75 + 0.25

Reorder the terms:
0.25 + 0.25y + y2 = -3.75 + 0.25

Combine like terms: -3.75 + 0.25 = -3.5
0.25 + 0.25y + y2 = -3.5

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -3.5

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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