a^2-az-2z^2=0

Solution for a^2-az-2z^2=0 equation:

Simplifying
a2 + -1az + -2z2 = 0

Reorder the terms:
-1az + a2 + -2z2 = 0

Solving
-1az + a2 + -2z2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -2z)(a + z) = 0

Subproblem 1
Set the factor '(a + -2z)' equal to zero and attempt to solve:

Simplifying
a + -2z = 0

Solving
a + -2z = 0

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

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

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

Simplifying
a = 2z
Subproblem 2
Set the factor '(a + z)' equal to zero and attempt to solve:

Simplifying
a + z = 0

Solving
a + z = 0

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

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

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

Simplifying
a = -1z
Solution
a = {2z, -1z}