y+5(4y+2)=10(y+1)9y

Solution for y+5(4y+2)=10(y+1)9y equation:

Simplifying
y + 5(4y + 2) = 10(y + 1) * 9y

Reorder the terms:
y + 5(2 + 4y) = 10(y + 1) * 9y
y + (2 * 5 + 4y * 5) = 10(y + 1) * 9y
y + (10 + 20y) = 10(y + 1) * 9y

Reorder the terms:
10 + y + 20y = 10(y + 1) * 9y

Combine like terms: y + 20y = 21y
10 + 21y = 10(y + 1) * 9y

Reorder the terms:
10 + 21y = 10(1 + y) * 9y

Reorder the terms for easier multiplication:
10 + 21y = 10 * 9y(1 + y)

Multiply 10 * 9
10 + 21y = 90y(1 + y)
10 + 21y = (1 * 90y + y * 90y)
10 + 21y = (90y + 90y2)

Solving
10 + 21y = 90y + 90y2

Solving for variable 'y'.

Combine like terms: 21y + -90y = -69y
10 + -69y + -90y2 = 90y + 90y2 + -90y + -90y2

Reorder the terms:
10 + -69y + -90y2 = 90y + -90y + 90y2 + -90y2

Combine like terms: 90y + -90y = 0
10 + -69y + -90y2 = 0 + 90y2 + -90y2
10 + -69y + -90y2 = 90y2 + -90y2

Combine like terms: 90y2 + -90y2 = 0
10 + -69y + -90y2 = 0

Begin completing the square.  Divide all terms by
-90 the coefficient of the squared term: 

Divide each side by '-90'.
-0.1111111111 + 0.7666666667y + y2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.7666666667y + 0.1111111111 + y2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 0.7666666667y + y2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 0.7666666667y + y2 = 0 + 0.1111111111
0.7666666667y + y2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
0.7666666667y + y2 = 0.1111111111

The y term is 0.7666666667y.  Take half its coefficient (0.3833333334).
Square it (0.1469444445) and add it to both sides.

Add '0.1469444445' to each side of the equation.
0.7666666667y + 0.1469444445 + y2 = 0.1111111111 + 0.1469444445

Reorder the terms:
0.1469444445 + 0.7666666667y + y2 = 0.1111111111 + 0.1469444445

Combine like terms: 0.1111111111 + 0.1469444445 = 0.2580555556
0.1469444445 + 0.7666666667y + y2 = 0.2580555556

Factor a perfect square on the left side:
(y + 0.3833333334)(y + 0.3833333334) = 0.2580555556

Calculate the square root of the right side: 0.507991689

Break this problem into two subproblems by setting 
(y + 0.3833333334) equal to 0.507991689 and -0.507991689.

Subproblem 1
y + 0.3833333334 = 0.507991689

Simplifying
y + 0.3833333334 = 0.507991689

Reorder the terms:
0.3833333334 + y = 0.507991689

Solving
0.3833333334 + y = 0.507991689

Solving for variable 'y'.

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

Add '-0.3833333334' to each side of the equation.
0.3833333334 + -0.3833333334 + y = 0.507991689 + -0.3833333334

Combine like terms: 0.3833333334 + -0.3833333334 = 0.0000000000
0.0000000000 + y = 0.507991689 + -0.3833333334
y = 0.507991689 + -0.3833333334

Combine like terms: 0.507991689 + -0.3833333334 = 0.1246583556
y = 0.1246583556

Simplifying
y = 0.1246583556

Subproblem 2
y + 0.3833333334 = -0.507991689

Simplifying
y + 0.3833333334 = -0.507991689

Reorder the terms:
0.3833333334 + y = -0.507991689

Solving
0.3833333334 + y = -0.507991689

Solving for variable 'y'.

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

Add '-0.3833333334' to each side of the equation.
0.3833333334 + -0.3833333334 + y = -0.507991689 + -0.3833333334

Combine like terms: 0.3833333334 + -0.3833333334 = 0.0000000000
0.0000000000 + y = -0.507991689 + -0.3833333334
y = -0.507991689 + -0.3833333334

Combine like terms: -0.507991689 + -0.3833333334 = -0.8913250224
y = -0.8913250224

Simplifying
y = -0.8913250224

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.1246583556, -0.8913250224}