5y^4=y^2(2z-7ax)

Solution for 5y^4=y^2(2z-7ax) equation:

Simplifying
5y4 = y2(2z + -7ax)

Reorder the terms:
5y4 = y2(-7ax + 2z)
5y4 = (-7ax * y2 + 2z * y2)
5y4 = (-7axy2 + 2y2z)

Solving
5y4 = -7axy2 + 2y2z

Solving for variable 'y'.

Reorder the terms:
7axy2 + -2y2z + 5y4 = -7axy2 + 2y2z + 7axy2 + -2y2z

Reorder the terms:
7axy2 + -2y2z + 5y4 = -7axy2 + 7axy2 + 2y2z + -2y2z

Combine like terms: -7axy2 + 7axy2 = 0
7axy2 + -2y2z + 5y4 = 0 + 2y2z + -2y2z
7axy2 + -2y2z + 5y4 = 2y2z + -2y2z

Combine like terms: 2y2z + -2y2z = 0
7axy2 + -2y2z + 5y4 = 0

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(7ax + -2z + 5y2) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(7ax + -2z + 5y2)' equal to zero and attempt to solve:

Simplifying
7ax + -2z + 5y2 = 0

Reorder the terms:
7ax + 5y2 + -2z = 0

Solving
7ax + 5y2 + -2z = 0

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

Add '-7ax' to each side of the equation.
7ax + 5y2 + -7ax + -2z = 0 + -7ax

Reorder the terms:
7ax + -7ax + 5y2 + -2z = 0 + -7ax

Combine like terms: 7ax + -7ax = 0
0 + 5y2 + -2z = 0 + -7ax
5y2 + -2z = 0 + -7ax
Remove the zero:
5y2 + -2z = -7ax

Add '2z' to each side of the equation.
5y2 + -2z + 2z = -7ax + 2z

Combine like terms: -2z + 2z = 0
5y2 + 0 = -7ax + 2z
5y2 = -7ax + 2z

Divide each side by '5'.
y2 = -1.4ax + 0.4z

Simplifying
y2 = -1.4ax + 0.4z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}