-3(y+1)*7y=4(y+1)-5

Solution for -3(y+1)*7y=4(y+1)-5 equation:

Simplifying
-3(y + 1) * 7y = 4(y + 1) + -5

Reorder the terms:
-3(1 + y) * 7y = 4(y + 1) + -5

Reorder the terms for easier multiplication:
-3 * 7y(1 + y) = 4(y + 1) + -5

Multiply -3 * 7
-21y(1 + y) = 4(y + 1) + -5
(1 * -21y + y * -21y) = 4(y + 1) + -5
(-21y + -21y2) = 4(y + 1) + -5

Reorder the terms:
-21y + -21y2 = 4(1 + y) + -5
-21y + -21y2 = (1 * 4 + y * 4) + -5
-21y + -21y2 = (4 + 4y) + -5

Reorder the terms:
-21y + -21y2 = 4 + -5 + 4y

Combine like terms: 4 + -5 = -1
-21y + -21y2 = -1 + 4y

Solving
-21y + -21y2 = -1 + 4y

Solving for variable 'y'.

Reorder the terms:
1 + -21y + -4y + -21y2 = -1 + 4y + 1 + -4y

Combine like terms: -21y + -4y = -25y
1 + -25y + -21y2 = -1 + 4y + 1 + -4y

Reorder the terms:
1 + -25y + -21y2 = -1 + 1 + 4y + -4y

Combine like terms: -1 + 1 = 0
1 + -25y + -21y2 = 0 + 4y + -4y
1 + -25y + -21y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
1 + -25y + -21y2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
-0.04761904762 + 1.19047619y + y2 = 0

Move the constant term to the right:

Add '0.04761904762' to each side of the equation.
-0.04761904762 + 1.19047619y + 0.04761904762 + y2 = 0 + 0.04761904762

Reorder the terms:
-0.04761904762 + 0.04761904762 + 1.19047619y + y2 = 0 + 0.04761904762

Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000
0.00000000000 + 1.19047619y + y2 = 0 + 0.04761904762
1.19047619y + y2 = 0 + 0.04761904762

Combine like terms: 0 + 0.04761904762 = 0.04761904762
1.19047619y + y2 = 0.04761904762

The y term is 1.19047619y.  Take half its coefficient (0.595238095).
Square it (0.3543083897) and add it to both sides.

Add '0.3543083897' to each side of the equation.
1.19047619y + 0.3543083897 + y2 = 0.04761904762 + 0.3543083897

Reorder the terms:
0.3543083897 + 1.19047619y + y2 = 0.04761904762 + 0.3543083897

Combine like terms: 0.04761904762 + 0.3543083897 = 0.40192743732
0.3543083897 + 1.19047619y + y2 = 0.40192743732

Factor a perfect square on the left side:
(y + 0.595238095)(y + 0.595238095) = 0.40192743732

Calculate the square root of the right side: 0.633977474

Break this problem into two subproblems by setting 
(y + 0.595238095) equal to 0.633977474 and -0.633977474.

Subproblem 1
y + 0.595238095 = 0.633977474

Simplifying
y + 0.595238095 = 0.633977474

Reorder the terms:
0.595238095 + y = 0.633977474

Solving
0.595238095 + y = 0.633977474

Solving for variable 'y'.

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

Add '-0.595238095' to each side of the equation.
0.595238095 + -0.595238095 + y = 0.633977474 + -0.595238095

Combine like terms: 0.595238095 + -0.595238095 = 0.000000000
0.000000000 + y = 0.633977474 + -0.595238095
y = 0.633977474 + -0.595238095

Combine like terms: 0.633977474 + -0.595238095 = 0.038739379
y = 0.038739379

Simplifying
y = 0.038739379

Subproblem 2
y + 0.595238095 = -0.633977474

Simplifying
y + 0.595238095 = -0.633977474

Reorder the terms:
0.595238095 + y = -0.633977474

Solving
0.595238095 + y = -0.633977474

Solving for variable 'y'.

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

Add '-0.595238095' to each side of the equation.
0.595238095 + -0.595238095 + y = -0.633977474 + -0.595238095

Combine like terms: 0.595238095 + -0.595238095 = 0.000000000
0.000000000 + y = -0.633977474 + -0.595238095
y = -0.633977474 + -0.595238095

Combine like terms: -0.633977474 + -0.595238095 = -1.229215569
y = -1.229215569

Simplifying
y = -1.229215569

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.038739379, -1.229215569}