3a=2*(3a*3a)-3*(3a)+4

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Solution for 3a=2*(3a*3a)-3*(3a)+4 equation: 


Simplifying
3a = 2(3a * 3a) + -3(3a) + 4

Reorder the terms for easier multiplication:
3a = 2(3 * 3a * a) + -3(3a) + 4

Multiply 3 * 3
3a = 2(9a * a) + -3(3a) + 4

Multiply a * a
3a = 2(9a2) + -3(3a) + 4

Remove parenthesis around (9a2)
3a = 2 * 9a2 + -3(3a) + 4

Multiply 2 * 9
3a = 18a2 + -3(3a) + 4

Remove parenthesis around (3a)
3a = 18a2 + -3 * 3a + 4

Multiply -3 * 3
3a = 18a2 + -9a + 4

Reorder the terms:
3a = 4 + -9a + 18a2

Solving
3a = 4 + -9a + 18a2

Solving for variable 'a'.

Reorder the terms:
-4 + 3a + 9a + -18a2 = 4 + -9a + 18a2 + -4 + 9a + -18a2

Combine like terms: 3a + 9a = 12a
-4 + 12a + -18a2 = 4 + -9a + 18a2 + -4 + 9a + -18a2

Reorder the terms:
-4 + 12a + -18a2 = 4 + -4 + -9a + 9a + 18a2 + -18a2

Combine like terms: 4 + -4 = 0
-4 + 12a + -18a2 = 0 + -9a + 9a + 18a2 + -18a2
-4 + 12a + -18a2 = -9a + 9a + 18a2 + -18a2

Combine like terms: -9a + 9a = 0
-4 + 12a + -18a2 = 0 + 18a2 + -18a2
-4 + 12a + -18a2 = 18a2 + -18a2

Combine like terms: 18a2 + -18a2 = 0
-4 + 12a + -18a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 6a + -9a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 6a + -9a2)' equal to zero and attempt to solve:

Simplifying
-2 + 6a + -9a2 = 0

Solving
-2 + 6a + -9a2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
0.2222222222 + -0.6666666667a + a2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.6666666667a + -0.2222222222 + a2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + -0.6666666667a + a2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + -0.6666666667a + a2 = 0 + -0.2222222222
-0.6666666667a + a2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
-0.6666666667a + a2 = -0.2222222222

The a term is -0.6666666667a.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667a + 0.1111111112 + a2 = -0.2222222222 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667a + a2 = -0.2222222222 + 0.1111111112

Combine like terms: -0.2222222222 + 0.1111111112 = -0.111111111
0.1111111112 + -0.6666666667a + a2 = -0.111111111

Factor a perfect square on the left side:
(a + -0.3333333334)(a + -0.3333333334) = -0.111111111

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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