10a^3b^2-58a^2b^2-84ab^2=0

Solution for 10a^3b^2-58a^2b^2-84ab^2=0 equation:

Simplifying
10a3b2 + -58a2b2 + -84ab2 = 0

Reorder the terms:
-84ab2 + -58a2b2 + 10a3b2 = 0

Solving
-84ab2 + -58a2b2 + 10a3b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2ab2'.
2ab2(-42 + -29a + 5a2) = 0

Factor a trinomial.
2ab2((-6 + -5a)(7 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'ab2' equal to zero and attempt to solve:

Simplifying
ab2 = 0

Solving
ab2 = 0

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

Simplifying
ab2 = 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 '(-6 + -5a)' equal to zero and attempt to solve:

Simplifying
-6 + -5a = 0

Solving
-6 + -5a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5a = 0 + 6
-5a = 0 + 6

Combine like terms: 0 + 6 = 6
-5a = 6

Divide each side by '-5'.
a = -1.2

Simplifying
a = -1.2
Subproblem 3
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-1.2, 7}