(2a^2+6a+14)+(-4a^2+3a-9)=

Solution for (2a^2+6a+14)+(-4a^2+3a-9)= equation:

Simplifying
(2a2 + 6a + 14) + (-4a2 + 3a + -9) = 0

Reorder the terms:
(14 + 6a + 2a2) + (-4a2 + 3a + -9) = 0

Remove parenthesis around (14 + 6a + 2a2)
14 + 6a + 2a2 + (-4a2 + 3a + -9) = 0

Reorder the terms:
14 + 6a + 2a2 + (-9 + 3a + -4a2) = 0

Remove parenthesis around (-9 + 3a + -4a2)
14 + 6a + 2a2 + -9 + 3a + -4a2 = 0

Reorder the terms:
14 + -9 + 6a + 3a + 2a2 + -4a2 = 0

Combine like terms: 14 + -9 = 5
5 + 6a + 3a + 2a2 + -4a2 = 0

Combine like terms: 6a + 3a = 9a
5 + 9a + 2a2 + -4a2 = 0

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

Solving
5 + 9a + -2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + -1a)(1 + 2a) = 0

Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {5, -0.5}