0=5(y-0.4)(y+2.1)

Solution for 0=5(y-0.4)(y+2.1) equation:

Simplifying
0 = 5(y + -0.4)(y + 2.1)

Reorder the terms:
0 = 5(-0.4 + y)(y + 2.1)

Reorder the terms:
0 = 5(-0.4 + y)(2.1 + y)

Multiply (-0.4 + y) * (2.1 + y)
0 = 5(-0.4(2.1 + y) + y(2.1 + y))
0 = 5((2.1 * -0.4 + y * -0.4) + y(2.1 + y))
0 = 5((-0.84 + -0.4y) + y(2.1 + y))
0 = 5(-0.84 + -0.4y + (2.1 * y + y * y))
0 = 5(-0.84 + -0.4y + (2.1y + y2))

Combine like terms: -0.4y + 2.1y = 1.7y
0 = 5(-0.84 + 1.7y + y2)
0 = (-0.84 * 5 + 1.7y * 5 + y2 * 5)
0 = (-4.2 + 8.5y + 5y2)

Solving
0 = -4.2 + 8.5y + 5y2

Solving for variable 'y'.

Combine like terms: 0 + 4.2 = 4.2
4.2 + -8.5y + -5y2 = -4.2 + 8.5y + 5y2 + 4.2 + -8.5y + -5y2

Reorder the terms:
4.2 + -8.5y + -5y2 = -4.2 + 4.2 + 8.5y + -8.5y + 5y2 + -5y2

Combine like terms: -4.2 + 4.2 = 0.0
4.2 + -8.5y + -5y2 = 0.0 + 8.5y + -8.5y + 5y2 + -5y2
4.2 + -8.5y + -5y2 = 8.5y + -8.5y + 5y2 + -5y2

Combine like terms: 8.5y + -8.5y = 0.0
4.2 + -8.5y + -5y2 = 0.0 + 5y2 + -5y2
4.2 + -8.5y + -5y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
4.2 + -8.5y + -5y2 = 0

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

Divide each side by '-5'.
-0.84 + 1.7y + y2 = 0

Move the constant term to the right:

Add '0.84' to each side of the equation.
-0.84 + 1.7y + 0.84 + y2 = 0 + 0.84

Reorder the terms:
-0.84 + 0.84 + 1.7y + y2 = 0 + 0.84

Combine like terms: -0.84 + 0.84 = 0.00
0.00 + 1.7y + y2 = 0 + 0.84
1.7y + y2 = 0 + 0.84

Combine like terms: 0 + 0.84 = 0.84
1.7y + y2 = 0.84

The y term is 1.7y.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7y + 0.7225 + y2 = 0.84 + 0.7225

Reorder the terms:
0.7225 + 1.7y + y2 = 0.84 + 0.7225

Combine like terms: 0.84 + 0.7225 = 1.5625
0.7225 + 1.7y + y2 = 1.5625

Factor a perfect square on the left side:
(y + 0.85)(y + 0.85) = 1.5625

Calculate the square root of the right side: 1.25

Break this problem into two subproblems by setting 
(y + 0.85) equal to 1.25 and -1.25.

Subproblem 1
y + 0.85 = 1.25

Simplifying
y + 0.85 = 1.25

Reorder the terms:
0.85 + y = 1.25

Solving
0.85 + y = 1.25

Solving for variable 'y'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + y = 1.25 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + y = 1.25 + -0.85
y = 1.25 + -0.85

Combine like terms: 1.25 + -0.85 = 0.4
y = 0.4

Simplifying
y = 0.4

Subproblem 2
y + 0.85 = -1.25

Simplifying
y + 0.85 = -1.25

Reorder the terms:
0.85 + y = -1.25

Solving
0.85 + y = -1.25

Solving for variable 'y'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + y = -1.25 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + y = -1.25 + -0.85
y = -1.25 + -0.85

Combine like terms: -1.25 + -0.85 = -2.1
y = -2.1

Simplifying
y = -2.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.4, -2.1}