21a^4-102a^3-144a^2=0

Solution for 21a^4-102a^3-144a^2=0 equation:

Simplifying
21a4 + -102a3 + -144a2 = 0

Reorder the terms:
-144a2 + -102a3 + 21a4 = 0

Solving
-144a2 + -102a3 + 21a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a2'.
3a2(-48 + -34a + 7a2) = 0

Factor a trinomial.
3a2((-8 + -7a)(6 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(-8 + -7a)' equal to zero and attempt to solve:

Simplifying
-8 + -7a = 0

Solving
-8 + -7a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7a = 0 + 8
-7a = 0 + 8

Combine like terms: 0 + 8 = 8
-7a = 8

Divide each side by '-7'.
a = -1.142857143

Simplifying
a = -1.142857143
Subproblem 3
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {0, -1.142857143, 6}