6ax^2+9ax+15a=3a

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Solution for 6ax^2+9ax+15a=3a equation: 


Simplifying
6ax2 + 9ax + 15a = 3a

Reorder the terms:
15a + 9ax + 6ax2 = 3a

Solving
15a + 9ax + 6ax2 = 3a

Solving for variable 'a'.

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

Add '-3a' to each side of the equation.
15a + 9ax + -3a + 6ax2 = 3a + -3a

Reorder the terms:
15a + -3a + 9ax + 6ax2 = 3a + -3a

Combine like terms: 15a + -3a = 12a
12a + 9ax + 6ax2 = 3a + -3a

Combine like terms: 3a + -3a = 0
12a + 9ax + 6ax2 = 0

Factor out the Greatest Common Factor (GCF), '3a'.
3a(4 + 3x + 2x2) = 0

Ignore the factor 3.

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 '(4 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
4 + 3x + 2x2 = 0

Solving
4 + 3x + 2x2 = 0

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

Add '-4' to each side of the equation.
4 + 3x + -4 + 2x2 = 0 + -4

Reorder the terms:
4 + -4 + 3x + 2x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x + 2x2 = 0 + -4
3x + 2x2 = 0 + -4

Combine like terms: 0 + -4 = -4
3x + 2x2 = -4

Add '-3x' to each side of the equation.
3x + -3x + 2x2 = -4 + -3x

Combine like terms: 3x + -3x = 0
0 + 2x2 = -4 + -3x
2x2 = -4 + -3x

Add '-2x2' to each side of the equation.
2x2 + -2x2 = -4 + -3x + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 = -4 + -3x + -2x2

Simplifying
0 = -4 + -3x + -2x2

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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