0.4y+0.8(4)=0.5y(y+4)

Solution for 0.4y+0.8(4)=0.5y(y+4) equation:

Simplifying
0.4y + 0.8(4) = 0.5y(y + 4)

Multiply 0.8 * 4
0.4y + 3.2 = 0.5y(y + 4)

Reorder the terms:
3.2 + 0.4y = 0.5y(y + 4)

Reorder the terms:
3.2 + 0.4y = 0.5y(4 + y)
3.2 + 0.4y = (4 * 0.5y + y * 0.5y)
3.2 + 0.4y = (2y + 0.5y2)

Solving
3.2 + 0.4y = 2y + 0.5y2

Solving for variable 'y'.

Combine like terms: 0.4y + -2y = -1.6y
3.2 + -1.6y + -0.5y2 = 2y + 0.5y2 + -2y + -0.5y2

Reorder the terms:
3.2 + -1.6y + -0.5y2 = 2y + -2y + 0.5y2 + -0.5y2

Combine like terms: 2y + -2y = 0
3.2 + -1.6y + -0.5y2 = 0 + 0.5y2 + -0.5y2
3.2 + -1.6y + -0.5y2 = 0.5y2 + -0.5y2

Combine like terms: 0.5y2 + -0.5y2 = 0.0
3.2 + -1.6y + -0.5y2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-6.4 + 3.2y + y2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + 3.2y + 6.4 + y2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + 3.2y + y2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + 3.2y + y2 = 0 + 6.4
3.2y + y2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
3.2y + y2 = 6.4

The y term is 3.2y.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2y + 2.56 + y2 = 6.4 + 2.56

Reorder the terms:
2.56 + 3.2y + y2 = 6.4 + 2.56

Combine like terms: 6.4 + 2.56 = 8.96
2.56 + 3.2y + y2 = 8.96

Factor a perfect square on the left side:
(y + 1.6)(y + 1.6) = 8.96

Calculate the square root of the right side: 2.993325909

Break this problem into two subproblems by setting 
(y + 1.6) equal to 2.993325909 and -2.993325909.

Subproblem 1
y + 1.6 = 2.993325909

Simplifying
y + 1.6 = 2.993325909

Reorder the terms:
1.6 + y = 2.993325909

Solving
1.6 + y = 2.993325909

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = 2.993325909 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = 2.993325909 + -1.6
y = 2.993325909 + -1.6

Combine like terms: 2.993325909 + -1.6 = 1.393325909
y = 1.393325909

Simplifying
y = 1.393325909

Subproblem 2
y + 1.6 = -2.993325909

Simplifying
y + 1.6 = -2.993325909

Reorder the terms:
1.6 + y = -2.993325909

Solving
1.6 + y = -2.993325909

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = -2.993325909 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = -2.993325909 + -1.6
y = -2.993325909 + -1.6

Combine like terms: -2.993325909 + -1.6 = -4.593325909
y = -4.593325909

Simplifying
y = -4.593325909

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.393325909, -4.593325909}