17-(4y-2)=2y(y+3)

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Solution for 17-(4y-2)=2y(y+3) equation:


Simplifying
17 + -1(4y + -2) = 2y(y + 3)

Reorder the terms:
17 + -1(-2 + 4y) = 2y(y + 3)
17 + (-2 * -1 + 4y * -1) = 2y(y + 3)
17 + (2 + -4y) = 2y(y + 3)

Combine like terms: 17 + 2 = 19
19 + -4y = 2y(y + 3)

Reorder the terms:
19 + -4y = 2y(3 + y)
19 + -4y = (3 * 2y + y * 2y)
19 + -4y = (6y + 2y2)

Solving
19 + -4y = 6y + 2y2

Solving for variable 'y'.

Combine like terms: -4y + -6y = -10y
19 + -10y + -2y2 = 6y + 2y2 + -6y + -2y2

Reorder the terms:
19 + -10y + -2y2 = 6y + -6y + 2y2 + -2y2

Combine like terms: 6y + -6y = 0
19 + -10y + -2y2 = 0 + 2y2 + -2y2
19 + -10y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
19 + -10y + -2y2 = 0

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

Divide each side by '-2'.
-9.5 + 5y + y2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 5y + 9.5 + y2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 5y + y2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 5y + y2 = 0 + 9.5
5y + y2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
5y + y2 = 9.5

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 9.5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 9.5 + 6.25

Combine like terms: 9.5 + 6.25 = 15.75
6.25 + 5y + y2 = 15.75

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(y + 2.5) equal to 3.968626967 and -3.968626967.


Subproblem 1
y + 2.5 = 3.968626967

Simplifying
y + 2.5 = 3.968626967

Reorder the terms:
2.5 + y = 3.968626967

Solving
2.5 + y = 3.968626967

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 3.968626967 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 3.968626967 + -2.5
y = 3.968626967 + -2.5

Combine like terms: 3.968626967 + -2.5 = 1.468626967
y = 1.468626967

Simplifying
y = 1.468626967


Subproblem 2
y + 2.5 = -3.968626967

Simplifying
y + 2.5 = -3.968626967

Reorder the terms:
2.5 + y = -3.968626967

Solving
2.5 + y = -3.968626967

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -3.968626967 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -3.968626967 + -2.5
y = -3.968626967 + -2.5

Combine like terms: -3.968626967 + -2.5 = -6.468626967
y = -6.468626967

Simplifying
y = -6.468626967


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.468626967, -6.468626967}

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