7y(y-3)=3y-45

Solution for 7y(y-3)=3y-45 equation:

Simplifying
7y(y + -3) = 3y + -45

Reorder the terms:
7y(-3 + y) = 3y + -45
(-3 * 7y + y * 7y) = 3y + -45
(-21y + 7y2) = 3y + -45

Reorder the terms:
-21y + 7y2 = -45 + 3y

Solving
-21y + 7y2 = -45 + 3y

Solving for variable 'y'.

Reorder the terms:
45 + -21y + -3y + 7y2 = -45 + 3y + 45 + -3y

Combine like terms: -21y + -3y = -24y
45 + -24y + 7y2 = -45 + 3y + 45 + -3y

Reorder the terms:
45 + -24y + 7y2 = -45 + 45 + 3y + -3y

Combine like terms: -45 + 45 = 0
45 + -24y + 7y2 = 0 + 3y + -3y
45 + -24y + 7y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
45 + -24y + 7y2 = 0

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

Divide each side by '7'.
6.428571429 + -3.428571429y + y2 = 0

Move the constant term to the right:

Add '-6.428571429' to each side of the equation.
6.428571429 + -3.428571429y + -6.428571429 + y2 = 0 + -6.428571429

Reorder the terms:
6.428571429 + -6.428571429 + -3.428571429y + y2 = 0 + -6.428571429

Combine like terms: 6.428571429 + -6.428571429 = 0.000000000
0.000000000 + -3.428571429y + y2 = 0 + -6.428571429
-3.428571429y + y2 = 0 + -6.428571429

Combine like terms: 0 + -6.428571429 = -6.428571429
-3.428571429y + y2 = -6.428571429

The y term is -3.428571429y.  Take half its coefficient (-1.714285715).
Square it (2.938775513) and add it to both sides.

Add '2.938775513' to each side of the equation.
-3.428571429y + 2.938775513 + y2 = -6.428571429 + 2.938775513

Reorder the terms:
2.938775513 + -3.428571429y + y2 = -6.428571429 + 2.938775513

Combine like terms: -6.428571429 + 2.938775513 = -3.489795916
2.938775513 + -3.428571429y + y2 = -3.489795916

Factor a perfect square on the left side:
(y + -1.714285715)(y + -1.714285715) = -3.489795916

Can't calculate square root of the right side.

The solution to this equation could not be determined.