((2y)((x^2)+7x-3))=0

Solution for ((2y)((x^2)+7x-3))=0 equation:

Simplifying
((2y)((x2) + 7x + -3)) = 0

Remove parenthesis around (2y)
(2y((x2) + 7x + -3)) = 0
(2y(x2 + 7x + -3)) = 0

Reorder the terms:
(2y(-3 + 7x + x2)) = 0
((-3 * 2y + 7x * 2y + x2 * 2y)) = 0

Reorder the terms:
((14xy + 2x2y + -6y)) = 0
((14xy + 2x2y + -6y)) = 0
(14xy + 2x2y + -6y) = 0

Remove parenthesis around (14xy + 2x2y + -6y)
14xy + 2x2y + -6y = 0

Solving
14xy + 2x2y + -6y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(7x + x2 + -3) = 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 + -3)' equal to zero and attempt to solve:

Simplifying
7x + x2 + -3 = 0

Reorder the terms:
-3 + 7x + x2 = 0

Solving
-3 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 7x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 7x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7x + x2 = 0 + 3
7x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
7x + x2 = 3

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 = 3 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 3 + 12.25

Combine like terms: 3 + 12.25 = 15.25
12.25 + 7x + x2 = 15.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
x + 3.5 = 3.905124838

Simplifying
x + 3.5 = 3.905124838

Reorder the terms:
3.5 + x = 3.905124838

Solving
3.5 + x = 3.905124838

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 = 3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.905124838 + -3.5
x = 3.905124838 + -3.5

Combine like terms: 3.905124838 + -3.5 = 0.405124838
x = 0.405124838

Simplifying
x = 0.405124838

Subproblem 2
x + 3.5 = -3.905124838

Simplifying
x + 3.5 = -3.905124838

Reorder the terms:
3.5 + x = -3.905124838

Solving
3.5 + x = -3.905124838

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 = -3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.905124838 + -3.5
x = -3.905124838 + -3.5

Combine like terms: -3.905124838 + -3.5 = -7.405124838
x = -7.405124838

Simplifying
x = -7.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.405124838, -7.405124838}
Solution
x = {0.405124838, -7.405124838}