6ax^2+4ax+10a=0

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Solution for 6ax^2+4ax+10a=0 equation: 


Simplifying
6ax2 + 4ax + 10a = 0

Reorder the terms:
10a + 4ax + 6ax2 = 0

Solving
10a + 4ax + 6ax2 = 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), '2a'.
2a(5 + 2x + 3x2) = 0

Ignore the factor 2.

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 '(5 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 2x + 3x2 = 0

Solving
5 + 2x + 3x2 = 0

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

Add '-5' to each side of the equation.
5 + 2x + -5 + 3x2 = 0 + -5

Reorder the terms:
5 + -5 + 2x + 3x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x + 3x2 = 0 + -5
2x + 3x2 = 0 + -5

Combine like terms: 0 + -5 = -5
2x + 3x2 = -5

Add '-2x' to each side of the equation.
2x + -2x + 3x2 = -5 + -2x

Combine like terms: 2x + -2x = 0
0 + 3x2 = -5 + -2x
3x2 = -5 + -2x

Add '-3x2' to each side of the equation.
3x2 + -3x2 = -5 + -2x + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 = -5 + -2x + -3x2

Simplifying
0 = -5 + -2x + -3x2

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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