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 = 0

Reorder the terms:
-75x3z2 + 15x4z + 18x5 = 0

Solving
-75x3z2 + 15x4z + 18x5 = 0

Solving for variable 'x'.

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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