18x^5+15x^4z=75x^3z^2

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Solution for 18x^5+15x^4z=75x^3z^2 equation: 


Simplifying
18x5 + 15x4z = 75x3z2

Reorder the terms:
15x4z + 18x5 = 75x3z2

Solving
15x4z + 18x5 = 75x3z2

Solving for variable 'x'.

Reorder the terms:
-75x3z2 + 15x4z + 18x5 = 75x3z2 + -75x3z2

Combine like terms: 75x3z2 + -75x3z2 = 0
-75x3z2 + 15x4z + 18x5 = 0

Factor out the Greatest Common Factor (GCF), '3x3'.
3x3(-25z2 + 5xz + 6x2) = 0

Factor a trinomial.
3x3((-5z + -2x)(5z + -3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

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 '(-5z + -2x)' equal to zero and attempt to solve:

Simplifying
-5z + -2x = 0

Reorder the terms:
-2x + -5z = 0

Solving
-2x + -5z = 0

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

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

Combine like terms: -5z + 5z = 0
-2x + 0 = 0 + 5z
-2x = 0 + 5z
Remove the zero:
-2x = 5z

Divide each side by '-2'.
x = -2.5z

Simplifying
x = -2.5z

Subproblem 3
Set the factor '(5z + -3x)' equal to zero and attempt to solve:

Simplifying
5z + -3x = 0

Reorder the terms:
-3x + 5z = 0

Solving
-3x + 5z = 0

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

Add '-5z' to each side of the equation.
-3x + 5z + -5z = 0 + -5z

Combine like terms: 5z + -5z = 0
-3x + 0 = 0 + -5z
-3x = 0 + -5z
Remove the zero:
-3x = -5z

Divide each side by '-3'.
x = 1.666666667z

Simplifying
x = 1.666666667z
Solution
x = {-2.5z, 1.666666667z}

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