a(3a-7)+(2a+3)2+3a^2=

Solution for a(3a-7)+(2a+3)2+3a^2= equation:

Simplifying
a(3a + -7) + (2a + 3) * 2 + 3a2 = 0

Reorder the terms:
a(-7 + 3a) + (2a + 3) * 2 + 3a2 = 0
(-7 * a + 3a * a) + (2a + 3) * 2 + 3a2 = 0
(-7a + 3a2) + (2a + 3) * 2 + 3a2 = 0

Reorder the terms:
-7a + 3a2 + (3 + 2a) * 2 + 3a2 = 0

Reorder the terms for easier multiplication:
-7a + 3a2 + 2(3 + 2a) + 3a2 = 0
-7a + 3a2 + (3 * 2 + 2a * 2) + 3a2 = 0
-7a + 3a2 + (6 + 4a) + 3a2 = 0

Reorder the terms:
6 + -7a + 4a + 3a2 + 3a2 = 0

Combine like terms: -7a + 4a = -3a
6 + -3a + 3a2 + 3a2 = 0

Combine like terms: 3a2 + 3a2 = 6a2
6 + -3a + 6a2 = 0

Solving
6 + -3a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1a + 2a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1a + 2a2)' equal to zero and attempt to solve:

Simplifying
2 + -1a + 2a2 = 0

Solving
2 + -1a + 2a2 = 0

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

Divide each side by '2'.
1 + -0.5a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.5a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + -0.5a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.5a + a2 = 0 + -1
-0.5a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.5a + a2 = -1

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = -1 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = -1 + 0.0625

Combine like terms: -1 + 0.0625 = -0.9375
0.0625 + -0.5a + a2 = -0.9375

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = -0.9375

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.