(4a^2+2a+14)-(3a^2+6a+11)=

Solution for (4a^2+2a+14)-(3a^2+6a+11)= equation:

Simplifying
(4a2 + 2a + 14) + -1(3a2 + 6a + 11) = 0

Reorder the terms:
(14 + 2a + 4a2) + -1(3a2 + 6a + 11) = 0

Remove parenthesis around (14 + 2a + 4a2)
14 + 2a + 4a2 + -1(3a2 + 6a + 11) = 0

Reorder the terms:
14 + 2a + 4a2 + -1(11 + 6a + 3a2) = 0
14 + 2a + 4a2 + (11 * -1 + 6a * -1 + 3a2 * -1) = 0
14 + 2a + 4a2 + (-11 + -6a + -3a2) = 0

Reorder the terms:
14 + -11 + 2a + -6a + 4a2 + -3a2 = 0

Combine like terms: 14 + -11 = 3
3 + 2a + -6a + 4a2 + -3a2 = 0

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

Combine like terms: 4a2 + -3a2 = 1a2
3 + -4a + 1a2 = 0

Solving
3 + -4a + 1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -1a)(3 + -1a) = 0

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

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

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

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

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {1, 3}