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Simplifying
4y2 + 8y + -21 = 0

Reorder the terms:
-21 + 8y + 4y2 = 0

Solving
-21 + 8y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
-5.25 + 2y + y2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + 2y + 5.25 + y2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + 2y + y2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + 2y + y2 = 0 + 5.25
2y + y2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
2y + y2 = 5.25

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 5.25 + 1

Reorder the terms:
1 + 2y + y2 = 5.25 + 1

Combine like terms: 5.25 + 1 = 6.25
1 + 2y + y2 = 6.25

Factor a perfect square on the left side:
(y + 1)(y + 1) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(y + 1) equal to 2.5 and -2.5.

Subproblem 1

y + 1 = 2.5 Simplifying y + 1 = 2.5 Reorder the terms: 1 + y = 2.5 Solving 1 + y = 2.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 2.5 + -1 Combine like terms: 1 + -1 = 0 0 + y = 2.5 + -1 y = 2.5 + -1 Combine like terms: 2.5 + -1 = 1.5 y = 1.5 Simplifying y = 1.5

Subproblem 2

y + 1 = -2.5 Simplifying y + 1 = -2.5 Reorder the terms: 1 + y = -2.5 Solving 1 + y = -2.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -2.5 + -1 Combine like terms: 1 + -1 = 0 0 + y = -2.5 + -1 y = -2.5 + -1 Combine like terms: -2.5 + -1 = -3.5 y = -3.5 Simplifying y = -3.5

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.5, -3.5}
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