100-(2y+12)(5y+6)=4-10y

Solution for 100-(2y+12)(5y+6)=4-10y equation:

Simplifying
100 + -1(2y + 12)(5y + 6) = 4 + -10y

Reorder the terms:
100 + -1(12 + 2y)(5y + 6) = 4 + -10y

Reorder the terms:
100 + -1(12 + 2y)(6 + 5y) = 4 + -10y

Multiply (12 + 2y) * (6 + 5y)
100 + -1(12(6 + 5y) + 2y * (6 + 5y)) = 4 + -10y
100 + -1((6 * 12 + 5y * 12) + 2y * (6 + 5y)) = 4 + -10y
100 + -1((72 + 60y) + 2y * (6 + 5y)) = 4 + -10y
100 + -1(72 + 60y + (6 * 2y + 5y * 2y)) = 4 + -10y
100 + -1(72 + 60y + (12y + 10y2)) = 4 + -10y

Combine like terms: 60y + 12y = 72y
100 + -1(72 + 72y + 10y2) = 4 + -10y
100 + (72 * -1 + 72y * -1 + 10y2 * -1) = 4 + -10y
100 + (-72 + -72y + -10y2) = 4 + -10y

Combine like terms: 100 + -72 = 28
28 + -72y + -10y2 = 4 + -10y

Solving
28 + -72y + -10y2 = 4 + -10y

Solving for variable 'y'.

Reorder the terms:
28 + -4 + -72y + 10y + -10y2 = 4 + -10y + -4 + 10y

Combine like terms: 28 + -4 = 24
24 + -72y + 10y + -10y2 = 4 + -10y + -4 + 10y

Combine like terms: -72y + 10y = -62y
24 + -62y + -10y2 = 4 + -10y + -4 + 10y

Reorder the terms:
24 + -62y + -10y2 = 4 + -4 + -10y + 10y

Combine like terms: 4 + -4 = 0
24 + -62y + -10y2 = 0 + -10y + 10y
24 + -62y + -10y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
24 + -62y + -10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -31y + -5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + -31y + -5y2)' equal to zero and attempt to solve:

Simplifying
12 + -31y + -5y2 = 0

Solving
12 + -31y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.4 + 6.2y + y2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 6.2y + 2.4 + y2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 6.2y + y2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 6.2y + y2 = 0 + 2.4
6.2y + y2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
6.2y + y2 = 2.4

The y term is 6.2y.  Take half its coefficient (3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
6.2y + 9.61 + y2 = 2.4 + 9.61

Reorder the terms:
9.61 + 6.2y + y2 = 2.4 + 9.61

Combine like terms: 2.4 + 9.61 = 12.01
9.61 + 6.2y + y2 = 12.01

Factor a perfect square on the left side:
(y + 3.1)(y + 3.1) = 12.01

Calculate the square root of the right side: 3.46554469

Break this problem into two subproblems by setting 
(y + 3.1) equal to 3.46554469 and -3.46554469.

Subproblem 1
y + 3.1 = 3.46554469

Simplifying
y + 3.1 = 3.46554469

Reorder the terms:
3.1 + y = 3.46554469

Solving
3.1 + y = 3.46554469

Solving for variable 'y'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + y = 3.46554469 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + y = 3.46554469 + -3.1
y = 3.46554469 + -3.1

Combine like terms: 3.46554469 + -3.1 = 0.36554469
y = 0.36554469

Simplifying
y = 0.36554469

Subproblem 2
y + 3.1 = -3.46554469

Simplifying
y + 3.1 = -3.46554469

Reorder the terms:
3.1 + y = -3.46554469

Solving
3.1 + y = -3.46554469

Solving for variable 'y'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + y = -3.46554469 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + y = -3.46554469 + -3.1
y = -3.46554469 + -3.1

Combine like terms: -3.46554469 + -3.1 = -6.56554469
y = -6.56554469

Simplifying
y = -6.56554469

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.36554469, -6.56554469}
Solution
y = {0.36554469, -6.56554469}