(2a^2+7a+1)-(3a^2+9a+7)=

Solution for (2a^2+7a+1)-(3a^2+9a+7)= equation:

Simplifying
(2a2 + 7a + 1) + -1(3a2 + 9a + 7) = 0

Reorder the terms:
(1 + 7a + 2a2) + -1(3a2 + 9a + 7) = 0

Remove parenthesis around (1 + 7a + 2a2)
1 + 7a + 2a2 + -1(3a2 + 9a + 7) = 0

Reorder the terms:
1 + 7a + 2a2 + -1(7 + 9a + 3a2) = 0
1 + 7a + 2a2 + (7 * -1 + 9a * -1 + 3a2 * -1) = 0
1 + 7a + 2a2 + (-7 + -9a + -3a2) = 0

Reorder the terms:
1 + -7 + 7a + -9a + 2a2 + -3a2 = 0

Combine like terms: 1 + -7 = -6
-6 + 7a + -9a + 2a2 + -3a2 = 0

Combine like terms: 7a + -9a = -2a
-6 + -2a + 2a2 + -3a2 = 0

Combine like terms: 2a2 + -3a2 = -1a2
-6 + -2a + -1a2 = 0

Solving
-6 + -2a + -1a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 2a + a2) = 0

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

Simplifying
6 + 2a + a2 = 0

Solving
6 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 2a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + 2a + a2 = 0 + -6

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

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

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = -6 + 1

Reorder the terms:
1 + 2a + a2 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + 2a + a2 = -5

Factor a perfect square on the left side:
(a + 1)(a + 1) = -5

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.