3ax^2+16ax+21a=0

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Solution for 3ax^2+16ax+21a=0 equation: 


Simplifying
3ax2 + 16ax + 21a = 0

Reorder the terms:
21a + 16ax + 3ax2 = 0

Solving
21a + 16ax + 3ax2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(21 + 16x + 3x2) = 0

Factor a trinomial.
a((3 + x)(7 + 3x)) = 0


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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Add '-1x' to each side of the equation.
x + -1x = -3 + -1x

Combine like terms: x + -1x = 0
0 = -3 + -1x

Simplifying
0 = -3 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Add '-3x' to each side of the equation.
3x + -3x = -7 + -3x

Combine like terms: 3x + -3x = 0
0 = -7 + -3x

Simplifying
0 = -7 + -3x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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