y+4(6y+4)=16(y+1)7y

Solution for y+4(6y+4)=16(y+1)7y equation:

Simplifying
y + 4(6y + 4) = 16(y + 1) * 7y

Reorder the terms:
y + 4(4 + 6y) = 16(y + 1) * 7y
y + (4 * 4 + 6y * 4) = 16(y + 1) * 7y
y + (16 + 24y) = 16(y + 1) * 7y

Reorder the terms:
16 + y + 24y = 16(y + 1) * 7y

Combine like terms: y + 24y = 25y
16 + 25y = 16(y + 1) * 7y

Reorder the terms:
16 + 25y = 16(1 + y) * 7y

Reorder the terms for easier multiplication:
16 + 25y = 16 * 7y(1 + y)

Multiply 16 * 7
16 + 25y = 112y(1 + y)
16 + 25y = (1 * 112y + y * 112y)
16 + 25y = (112y + 112y2)

Solving
16 + 25y = 112y + 112y2

Solving for variable 'y'.

Combine like terms: 25y + -112y = -87y
16 + -87y + -112y2 = 112y + 112y2 + -112y + -112y2

Reorder the terms:
16 + -87y + -112y2 = 112y + -112y + 112y2 + -112y2

Combine like terms: 112y + -112y = 0
16 + -87y + -112y2 = 0 + 112y2 + -112y2
16 + -87y + -112y2 = 112y2 + -112y2

Combine like terms: 112y2 + -112y2 = 0
16 + -87y + -112y2 = 0

Begin completing the square.  Divide all terms by
-112 the coefficient of the squared term: 

Divide each side by '-112'.
-0.1428571429 + 0.7767857143y + y2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.7767857143y + 0.1428571429 + y2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.7767857143y + y2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.7767857143y + y2 = 0 + 0.1428571429
0.7767857143y + y2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.7767857143y + y2 = 0.1428571429

The y term is 0.7767857143y.  Take half its coefficient (0.3883928572).
Square it (0.1508490115) and add it to both sides.

Add '0.1508490115' to each side of the equation.
0.7767857143y + 0.1508490115 + y2 = 0.1428571429 + 0.1508490115

Reorder the terms:
0.1508490115 + 0.7767857143y + y2 = 0.1428571429 + 0.1508490115

Combine like terms: 0.1428571429 + 0.1508490115 = 0.2937061544
0.1508490115 + 0.7767857143y + y2 = 0.2937061544

Factor a perfect square on the left side:
(y + 0.3883928572)(y + 0.3883928572) = 0.2937061544

Calculate the square root of the right side: 0.541946634

Break this problem into two subproblems by setting 
(y + 0.3883928572) equal to 0.541946634 and -0.541946634.

Subproblem 1
y + 0.3883928572 = 0.541946634

Simplifying
y + 0.3883928572 = 0.541946634

Reorder the terms:
0.3883928572 + y = 0.541946634

Solving
0.3883928572 + y = 0.541946634

Solving for variable 'y'.

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

Add '-0.3883928572' to each side of the equation.
0.3883928572 + -0.3883928572 + y = 0.541946634 + -0.3883928572

Combine like terms: 0.3883928572 + -0.3883928572 = 0.0000000000
0.0000000000 + y = 0.541946634 + -0.3883928572
y = 0.541946634 + -0.3883928572

Combine like terms: 0.541946634 + -0.3883928572 = 0.1535537768
y = 0.1535537768

Simplifying
y = 0.1535537768

Subproblem 2
y + 0.3883928572 = -0.541946634

Simplifying
y + 0.3883928572 = -0.541946634

Reorder the terms:
0.3883928572 + y = -0.541946634

Solving
0.3883928572 + y = -0.541946634

Solving for variable 'y'.

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

Add '-0.3883928572' to each side of the equation.
0.3883928572 + -0.3883928572 + y = -0.541946634 + -0.3883928572

Combine like terms: 0.3883928572 + -0.3883928572 = 0.0000000000
0.0000000000 + y = -0.541946634 + -0.3883928572
y = -0.541946634 + -0.3883928572

Combine like terms: -0.541946634 + -0.3883928572 = -0.9303394912
y = -0.9303394912

Simplifying
y = -0.9303394912

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.1535537768, -0.9303394912}