8x^2y+34xy-84y=0

Solution for 8x^2y+34xy-84y=0 equation:

Simplifying
8x2y + 34xy + -84y = 0

Reorder the terms:
34xy + 8x2y + -84y = 0

Solving
34xy + 8x2y + -84y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(17x + 4x2 + -42) = 0

Factor a trinomial.
2y((4x + -7)(x + 6)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4x + -7)' equal to zero and attempt to solve:

Simplifying
4x + -7 = 0

Reorder the terms:
-7 + 4x = 0

Solving
-7 + 4x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4x = 0 + 7
4x = 0 + 7

Combine like terms: 0 + 7 = 7
4x = 7

Divide each side by '4'.
x = 1.75

Simplifying
x = 1.75
Subproblem 3
Set the factor '(x + 6)' equal to zero and attempt to solve:

Simplifying
x + 6 = 0

Reorder the terms:
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {1.75, -6}