a^2b-3ab-10b=0

Solution for a^2b-3ab-10b=0 equation:

Simplifying
a2b + -3ab + -10b = 0

Reorder the terms:
-3ab + a2b + -10b = 0

Solving
-3ab + a2b + -10b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(-3a + a2 + -10) = 0

Factor a trinomial.
b((a + -5)(a + 2)) = 0

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

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

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 '(a + -5)' equal to zero and attempt to solve:

Simplifying
a + -5 = 0

Reorder the terms:
-5 + a = 0

Solving
-5 + a = 0

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

Add '5' to each side of the equation.
-5 + 5 + a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + a = 0 + 5
a = 0 + 5

Combine like terms: 0 + 5 = 5
a = 5

Simplifying
a = 5
Subproblem 3
Set the factor '(a + 2)' equal to zero and attempt to solve:

Simplifying
a + 2 = 0

Reorder the terms:
2 + a = 0

Solving
2 + a = 0

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

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

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Solution
a = {5, -2}