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

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Solution for 3a(3a)+4a=2a(2a)-2a-9 equation: 


Simplifying
3a(3a) + 4a = 2a(2a) + -2a + -9

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

Reorder the terms for easier multiplication:
3 * 3a * a + 4a = 2a(2a) + -2a + -9

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

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

Reorder the terms:
4a + 9a2 = 2a(2a) + -2a + -9

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

Reorder the terms for easier multiplication:
4a + 9a2 = 2 * 2a * a + -2a + -9

Multiply 2 * 2
4a + 9a2 = 4a * a + -2a + -9

Multiply a * a
4a + 9a2 = 4a2 + -2a + -9

Reorder the terms:
4a + 9a2 = -9 + -2a + 4a2

Solving
4a + 9a2 = -9 + -2a + 4a2

Solving for variable 'a'.

Reorder the terms:
9 + 4a + 2a + 9a2 + -4a2 = -9 + -2a + 4a2 + 9 + 2a + -4a2

Combine like terms: 4a + 2a = 6a
9 + 6a + 9a2 + -4a2 = -9 + -2a + 4a2 + 9 + 2a + -4a2

Combine like terms: 9a2 + -4a2 = 5a2
9 + 6a + 5a2 = -9 + -2a + 4a2 + 9 + 2a + -4a2

Reorder the terms:
9 + 6a + 5a2 = -9 + 9 + -2a + 2a + 4a2 + -4a2

Combine like terms: -9 + 9 = 0
9 + 6a + 5a2 = 0 + -2a + 2a + 4a2 + -4a2
9 + 6a + 5a2 = -2a + 2a + 4a2 + -4a2

Combine like terms: -2a + 2a = 0
9 + 6a + 5a2 = 0 + 4a2 + -4a2
9 + 6a + 5a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
9 + 6a + 5a2 = 0

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

Divide each side by '5'.
1.8 + 1.2a + a2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + 1.2a + -1.8 + a2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + 1.2a + a2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + 1.2a + a2 = 0 + -1.8
1.2a + a2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
1.2a + a2 = -1.8

The a term is 1.2a.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2a + 0.36 + a2 = -1.8 + 0.36

Reorder the terms:
0.36 + 1.2a + a2 = -1.8 + 0.36

Combine like terms: -1.8 + 0.36 = -1.44
0.36 + 1.2a + a2 = -1.44

Factor a perfect square on the left side:
(a + 0.6)(a + 0.6) = -1.44

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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