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

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


Simplifying
6ax2 + 4ax + 10a = 2a

Reorder the terms:
10a + 4ax + 6ax2 = 2a

Solving
10a + 4ax + 6ax2 = 2a

Solving for variable 'a'.

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

Add '-2a' to each side of the equation.
10a + 4ax + -2a + 6ax2 = 2a + -2a

Reorder the terms:
10a + -2a + 4ax + 6ax2 = 2a + -2a

Combine like terms: 10a + -2a = 8a
8a + 4ax + 6ax2 = 2a + -2a

Combine like terms: 2a + -2a = 0
8a + 4ax + 6ax2 = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(4 + 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 '(4 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 2x + 3x2 = 0

Solving
4 + 2x + 3x2 = 0

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

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

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

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

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

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

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

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

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

Simplifying
0 = -4 + -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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