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

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

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

Reorder the terms:
3y + -4y(-2 + y) = 15 + -3(y + -2)
3y + (-2 * -4y + y * -4y) = 15 + -3(y + -2)
3y + (8y + -4y2) = 15 + -3(y + -2)

Combine like terms: 3y + 8y = 11y
11y + -4y2 = 15 + -3(y + -2)

Reorder the terms:
11y + -4y2 = 15 + -3(-2 + y)
11y + -4y2 = 15 + (-2 * -3 + y * -3)
11y + -4y2 = 15 + (6 + -3y)

Combine like terms: 15 + 6 = 21
11y + -4y2 = 21 + -3y

Solving
11y + -4y2 = 21 + -3y

Solving for variable 'y'.

Reorder the terms:
-21 + 11y + 3y + -4y2 = 21 + -3y + -21 + 3y

Combine like terms: 11y + 3y = 14y
-21 + 14y + -4y2 = 21 + -3y + -21 + 3y

Reorder the terms:
-21 + 14y + -4y2 = 21 + -21 + -3y + 3y

Combine like terms: 21 + -21 = 0
-21 + 14y + -4y2 = 0 + -3y + 3y
-21 + 14y + -4y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
-21 + 14y + -4y2 = 0

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

Divide each side by '-4'.
5.25 + -3.5y + y2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -3.5y + -5.25 + y2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -3.5y + y2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -3.5y + y2 = 0 + -5.25
-3.5y + y2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-3.5y + y2 = -5.25

The y term is -3.5y.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5y + 3.0625 + y2 = -5.25 + 3.0625

Reorder the terms:
3.0625 + -3.5y + y2 = -5.25 + 3.0625

Combine like terms: -5.25 + 3.0625 = -2.1875
3.0625 + -3.5y + y2 = -2.1875

Factor a perfect square on the left side:
(y + -1.75)(y + -1.75) = -2.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.