0=y^2+17y-84

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Solution for 0=y^2+17y-84 equation: 


Simplifying
0 = y2 + 17y + -84

Reorder the terms:
0 = -84 + 17y + y2

Solving
0 = -84 + 17y + y2

Solving for variable 'y'.

Combine like terms: 0 + 84 = 84
84 + -17y + -1y2 = -84 + 17y + y2 + 84 + -17y + -1y2

Reorder the terms:
84 + -17y + -1y2 = -84 + 84 + 17y + -17y + y2 + -1y2

Combine like terms: -84 + 84 = 0
84 + -17y + -1y2 = 0 + 17y + -17y + y2 + -1y2
84 + -17y + -1y2 = 17y + -17y + y2 + -1y2

Combine like terms: 17y + -17y = 0
84 + -17y + -1y2 = 0 + y2 + -1y2
84 + -17y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
84 + -17y + -1y2 = 0

Factor a trinomial.
(4 + -1y)(21 + y) = 0


Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4

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

Simplifying
21 + y = 0

Solving
21 + y = 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 + y = 0 + -21

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

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

Simplifying
y = -21
Solution
y = {4, -21}

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