20ax^2+16ax+12a=4a

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Solution for 20ax^2+16ax+12a=4a equation: 


Simplifying
20ax2 + 16ax + 12a = 4a

Reorder the terms:
12a + 16ax + 20ax2 = 4a

Solving
12a + 16ax + 20ax2 = 4a

Solving for variable 'a'.

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

Add '-4a' to each side of the equation.
12a + 16ax + -4a + 20ax2 = 4a + -4a

Reorder the terms:
12a + -4a + 16ax + 20ax2 = 4a + -4a

Combine like terms: 12a + -4a = 8a
8a + 16ax + 20ax2 = 4a + -4a

Combine like terms: 4a + -4a = 0
8a + 16ax + 20ax2 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(2 + 4x + 5x2) = 0

Ignore the factor 4.

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 '(2 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + 4x + 5x2 = 0

Solving
2 + 4x + 5x2 = 0

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

Add '-2' to each side of the equation.
2 + 4x + -2 + 5x2 = 0 + -2

Reorder the terms:
2 + -2 + 4x + 5x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4x + 5x2 = 0 + -2
4x + 5x2 = 0 + -2

Combine like terms: 0 + -2 = -2
4x + 5x2 = -2

Add '-4x' to each side of the equation.
4x + -4x + 5x2 = -2 + -4x

Combine like terms: 4x + -4x = 0
0 + 5x2 = -2 + -4x
5x2 = -2 + -4x

Add '-5x2' to each side of the equation.
5x2 + -5x2 = -2 + -4x + -5x2

Combine like terms: 5x2 + -5x2 = 0
0 = -2 + -4x + -5x2

Simplifying
0 = -2 + -4x + -5x2

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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