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

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


Simplifying
16a2x2 + 20a2x + 12a2 = 4a2

Reorder the terms:
12a2 + 20a2x + 16a2x2 = 4a2

Solving
12a2 + 20a2x + 16a2x2 = 4a2

Solving for variable 'a'.

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

Add '-4a2' to each side of the equation.
12a2 + 20a2x + -4a2 + 16a2x2 = 4a2 + -4a2

Reorder the terms:
12a2 + -4a2 + 20a2x + 16a2x2 = 4a2 + -4a2

Combine like terms: 12a2 + -4a2 = 8a2
8a2 + 20a2x + 16a2x2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
8a2 + 20a2x + 16a2x2 = 0

Factor out the Greatest Common Factor (GCF), '4a2'.
4a2(2 + 5x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}

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

Simplifying
2 + 5x + 4x2 = 0

Solving
2 + 5x + 4x2 = 0

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

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

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

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

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

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

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

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

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

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

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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