2y(x^2+7x-23)=0

Solution for 2y(x^2+7x-23)=0 equation:

Simplifying
2y(x2 + 7x + -23) = 0

Reorder the terms:
2y(-23 + 7x + x2) = 0
(-23 * 2y + 7x * 2y + x2 * 2y) = 0

Reorder the terms:
(14xy + 2x2y + -46y) = 0
(14xy + 2x2y + -46y) = 0

Solving
14xy + 2x2y + -46y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(7x + x2 + -23) = 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 '(7x + x2 + -23)' equal to zero and attempt to solve:

Simplifying
7x + x2 + -23 = 0

Reorder the terms:
-23 + 7x + x2 = 0

Solving
-23 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 7x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 7x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 7x + x2 = 0 + 23
7x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
7x + x2 = 23

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 23 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 23 + 12.25

Combine like terms: 23 + 12.25 = 35.25
12.25 + 7x + x2 = 35.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.937171044 and -5.937171044.

Subproblem 1
x + 3.5 = 5.937171044

Simplifying
x + 3.5 = 5.937171044

Reorder the terms:
3.5 + x = 5.937171044

Solving
3.5 + x = 5.937171044

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.937171044 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.937171044 + -3.5
x = 5.937171044 + -3.5

Combine like terms: 5.937171044 + -3.5 = 2.437171044
x = 2.437171044

Simplifying
x = 2.437171044

Subproblem 2
x + 3.5 = -5.937171044

Simplifying
x + 3.5 = -5.937171044

Reorder the terms:
3.5 + x = -5.937171044

Solving
3.5 + x = -5.937171044

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.937171044 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.937171044 + -3.5
x = -5.937171044 + -3.5

Combine like terms: -5.937171044 + -3.5 = -9.437171044
x = -9.437171044

Simplifying
x = -9.437171044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.437171044, -9.437171044}
Solution
x = {2.437171044, -9.437171044}