a^2+2a-17=7

Solution for a^2+2a-17=7 equation:

Simplifying
a2 + 2a + -17 = 7

Reorder the terms:
-17 + 2a + a2 = 7

Solving
-17 + 2a + a2 = 7

Solving for variable 'a'.

Reorder the terms:
-17 + -7 + 2a + a2 = 7 + -7

Combine like terms: -17 + -7 = -24
-24 + 2a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-24 + 2a + a2 = 0

Factor a trinomial.
(-6 + -1a)(4 + -1a) = 0

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

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 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 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
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
Solution
a = {-6, 4}