y^2+40y-84=0

Solution for y^2+40y-84=0 equation:

Simplifying
y2 + 40y + -84 = 0

Reorder the terms:
-84 + 40y + y2 = 0

Solving
-84 + 40y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-42 + -1y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-42 + -1y)' equal to zero and attempt to solve:

Simplifying
-42 + -1y = 0

Solving
-42 + -1y = 0

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

Add '42' to each side of the equation.
-42 + 42 + -1y = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -1y = 0 + 42
-1y = 0 + 42

Combine like terms: 0 + 42 = 42
-1y = 42

Divide each side by '-1'.
y = -42

Simplifying
y = -42
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-42, 2}