14a^2=-21-49a

Solution for 14a^2=-21-49a equation:

Simplifying
14a2 = -21 + -49a

Solving
14a2 = -21 + -49a

Solving for variable 'a'.

Reorder the terms:
21 + 49a + 14a2 = -21 + -49a + 21 + 49a

Reorder the terms:
21 + 49a + 14a2 = -21 + 21 + -49a + 49a

Combine like terms: -21 + 21 = 0
21 + 49a + 14a2 = 0 + -49a + 49a
21 + 49a + 14a2 = -49a + 49a

Combine like terms: -49a + 49a = 0
21 + 49a + 14a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + 7a + 2a2) = 0

Factor a trinomial.
7((3 + a)(1 + 2a)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
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 = {-3, -0.5}