a^2+2a-22=-7

Solution for a^2+2a-22=-7 equation:

Simplifying
a2 + 2a + -22 = -7

Reorder the terms:
-22 + 2a + a2 = -7

Solving
-22 + 2a + a2 = -7

Solving for variable 'a'.

Reorder the terms:
-22 + 7 + 2a + a2 = -7 + 7

Combine like terms: -22 + 7 = -15
-15 + 2a + a2 = -7 + 7

Combine like terms: -7 + 7 = 0
-15 + 2a + a2 = 0

Factor a trinomial.
(-5 + -1a)(3 + -1a) = 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 '(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 = {-5, 3}