7x^2y+91xy-21y=0

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Solution for 7x^2y+91xy-21y=0 equation: 


Simplifying
7x2y + 91xy + -21y = 0

Reorder the terms:
91xy + 7x2y + -21y = 0

Solving
91xy + 7x2y + -21y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7y'.
7y(13x + x2 + -3) = 0

Ignore the factor 7.

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 '(13x + x2 + -3)' equal to zero and attempt to solve:

Simplifying
13x + x2 + -3 = 0

Reorder the terms:
-3 + 13x + x2 = 0

Solving
-3 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 13x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 13x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 13x + x2 = 0 + 3
13x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
13x + x2 = 3

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 3 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 3 + 42.25

Combine like terms: 3 + 42.25 = 45.25
42.25 + 13x + x2 = 45.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.726812024 and -6.726812024.


Subproblem 1
x + 6.5 = 6.726812024

Simplifying
x + 6.5 = 6.726812024

Reorder the terms:
6.5 + x = 6.726812024

Solving
6.5 + x = 6.726812024

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.726812024 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.726812024 + -6.5
x = 6.726812024 + -6.5

Combine like terms: 6.726812024 + -6.5 = 0.226812024
x = 0.226812024

Simplifying
x = 0.226812024


Subproblem 2
x + 6.5 = -6.726812024

Simplifying
x + 6.5 = -6.726812024

Reorder the terms:
6.5 + x = -6.726812024

Solving
6.5 + x = -6.726812024

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.726812024 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.726812024 + -6.5
x = -6.726812024 + -6.5

Combine like terms: -6.726812024 + -6.5 = -13.226812024
x = -13.226812024

Simplifying
x = -13.226812024


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.226812024, -13.226812024}
Solution
x = {0.226812024, -13.226812024}

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