a^2+3a+3=7

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

Simplifying
a2 + 3a + 3 = 7

Reorder the terms:
3 + 3a + a2 = 7

Solving
3 + 3a + a2 = 7

Solving for variable 'a'.

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

Combine like terms: 3 + -7 = -4
-4 + 3a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-4 + 3a + a2 = 0

Factor a trinomial.
(-4 + -1a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

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

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

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 2
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
Solution
a = {-4, 1}