3a^2+2a+21=-7a+3+2a^2

Solution for 3a^2+2a+21=-7a+3+2a^2 equation:

Simplifying
3a2 + 2a + 21 = -7a + 3 + 2a2

Reorder the terms:
21 + 2a + 3a2 = -7a + 3 + 2a2

Reorder the terms:
21 + 2a + 3a2 = 3 + -7a + 2a2

Solving
21 + 2a + 3a2 = 3 + -7a + 2a2

Solving for variable 'a'.

Reorder the terms:
21 + -3 + 2a + 7a + 3a2 + -2a2 = 3 + -7a + 2a2 + -3 + 7a + -2a2

Combine like terms: 21 + -3 = 18
18 + 2a + 7a + 3a2 + -2a2 = 3 + -7a + 2a2 + -3 + 7a + -2a2

Combine like terms: 2a + 7a = 9a
18 + 9a + 3a2 + -2a2 = 3 + -7a + 2a2 + -3 + 7a + -2a2

Combine like terms: 3a2 + -2a2 = 1a2
18 + 9a + 1a2 = 3 + -7a + 2a2 + -3 + 7a + -2a2

Reorder the terms:
18 + 9a + 1a2 = 3 + -3 + -7a + 7a + 2a2 + -2a2

Combine like terms: 3 + -3 = 0
18 + 9a + 1a2 = 0 + -7a + 7a + 2a2 + -2a2
18 + 9a + 1a2 = -7a + 7a + 2a2 + -2a2

Combine like terms: -7a + 7a = 0
18 + 9a + 1a2 = 0 + 2a2 + -2a2
18 + 9a + 1a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
18 + 9a + 1a2 = 0

Factor a trinomial.
(6 + a)(3 + a) = 0

Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

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

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

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

Simplifying
a = -6
Subproblem 2
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
Solution
a = {-6, -3}