4y^2-40y-21=0

Solution for 4y^2-40y-21=0 equation:

Simplifying
4y2 + -40y + -21 = 0

Reorder the terms:
-21 + -40y + 4y2 = 0

Solving
-21 + -40y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -2y)(21 + -2y) = 0

Subproblem 1
Set the factor '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2y = 0 + 1
-2y = 0 + 1

Combine like terms: 0 + 1 = 1
-2y = 1

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(21 + -2y)' equal to zero and attempt to solve:

Simplifying
21 + -2y = 0

Solving
21 + -2y = 0

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

Add '-21' to each side of the equation.
21 + -21 + -2y = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -2y = 0 + -21
-2y = 0 + -21

Combine like terms: 0 + -21 = -21
-2y = -21

Divide each side by '-2'.
y = 10.5

Simplifying
y = 10.5
Solution
y = {-0.5, 10.5}