0=(2z^4-3y)(2z^4-3y)

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Solution for 0=(2z^4-3y)(2z^4-3y) equation: 


Simplifying
0 = (2z4 + -3y)(2z4 + -3y)

Reorder the terms:
0 = (-3y + 2z4)(2z4 + -3y)

Reorder the terms:
0 = (-3y + 2z4)(-3y + 2z4)

Multiply (-3y + 2z4) * (-3y + 2z4)
0 = (-3y * (-3y + 2z4) + 2z4 * (-3y + 2z4))
0 = ((-3y * -3y + 2z4 * -3y) + 2z4 * (-3y + 2z4))

Reorder the terms:
0 = ((-6yz4 + 9y2) + 2z4 * (-3y + 2z4))
0 = ((-6yz4 + 9y2) + 2z4 * (-3y + 2z4))
0 = (-6yz4 + 9y2 + (-3y * 2z4 + 2z4 * 2z4))
0 = (-6yz4 + 9y2 + (-6yz4 + 4z8))

Reorder the terms:
0 = (-6yz4 + -6yz4 + 9y2 + 4z8)

Combine like terms: -6yz4 + -6yz4 = -12yz4
0 = (-12yz4 + 9y2 + 4z8)

Solving
0 = -12yz4 + 9y2 + 4z8

Solving for variable 'y'.
Remove the zero:
12yz4 + -9y2 + -4z8 = -12yz4 + 9y2 + 4z8 + 12yz4 + -9y2 + -4z8

Reorder the terms:
12yz4 + -9y2 + -4z8 = -12yz4 + 12yz4 + 9y2 + -9y2 + 4z8 + -4z8

Combine like terms: -12yz4 + 12yz4 = 0
12yz4 + -9y2 + -4z8 = 0 + 9y2 + -9y2 + 4z8 + -4z8
12yz4 + -9y2 + -4z8 = 9y2 + -9y2 + 4z8 + -4z8

Combine like terms: 9y2 + -9y2 = 0
12yz4 + -9y2 + -4z8 = 0 + 4z8 + -4z8
12yz4 + -9y2 + -4z8 = 4z8 + -4z8

Combine like terms: 4z8 + -4z8 = 0
12yz4 + -9y2 + -4z8 = 0

Factor a trinomial.
(-3y + 2z4)(3y + -2z4) = 0


Subproblem 1
Set the factor '(-3y + 2z4)' equal to zero and attempt to solve:

Simplifying
-3y + 2z4 = 0

Solving
-3y + 2z4 = 0

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

Add '-2z4' to each side of the equation.
-3y + 2z4 + -2z4 = 0 + -2z4

Combine like terms: 2z4 + -2z4 = 0
-3y + 0 = 0 + -2z4
-3y = 0 + -2z4
Remove the zero:
-3y = -2z4

Divide each side by '-3'.
y = 0.6666666667z4

Simplifying
y = 0.6666666667z4

Subproblem 2
Set the factor '(3y + -2z4)' equal to zero and attempt to solve:

Simplifying
3y + -2z4 = 0

Solving
3y + -2z4 = 0

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

Add '2z4' to each side of the equation.
3y + -2z4 + 2z4 = 0 + 2z4

Combine like terms: -2z4 + 2z4 = 0
3y + 0 = 0 + 2z4
3y = 0 + 2z4
Remove the zero:
3y = 2z4

Divide each side by '3'.
y = 0.6666666667z4

Simplifying
y = 0.6666666667z4
Solution
y = {0.6666666667z4, 0.6666666667z4}

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