z^2+9zx-10x^2=0

Solution for z^2+9zx-10x^2=0 equation:

Simplifying
z2 + 9zx + -10x2 = 0

Reorder the terms:
9xz + -10x2 + z2 = 0

Solving
9xz + -10x2 + z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10x + -1z)(x + -1z) = 0

Subproblem 1
Set the factor '(-10x + -1z)' equal to zero and attempt to solve:

Simplifying
-10x + -1z = 0

Solving
-10x + -1z = 0

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

Add 'z' to each side of the equation.
-10x + -1z + z = 0 + z

Combine like terms: -1z + z = 0
-10x + 0 = 0 + z
-10x = 0 + z
Remove the zero:
-10x = z

Divide each side by '-10'.
x = -0.1z

Simplifying
x = -0.1z
Subproblem 2
Set the factor '(x + -1z)' equal to zero and attempt to solve:

Simplifying
x + -1z = 0

Solving
x + -1z = 0

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

Add 'z' to each side of the equation.
x + -1z + z = 0 + z

Combine like terms: -1z + z = 0
x + 0 = 0 + z
x = 0 + z
Remove the zero:
x = z

Simplifying
x = z
Solution
x = {-0.1z, z}