a^2+14a-61=-10

Solution for a^2+14a-61=-10 equation:

Simplifying
a2 + 14a + -61 = -10

Reorder the terms:
-61 + 14a + a2 = -10

Solving
-61 + 14a + a2 = -10

Solving for variable 'a'.

Reorder the terms:
-61 + 10 + 14a + a2 = -10 + 10

Combine like terms: -61 + 10 = -51
-51 + 14a + a2 = -10 + 10

Combine like terms: -10 + 10 = 0
-51 + 14a + a2 = 0

Factor a trinomial.
(-17 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-17 + -1a)' equal to zero and attempt to solve:

Simplifying
-17 + -1a = 0

Solving
-17 + -1a = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1a = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1a = 0 + 17
-1a = 0 + 17

Combine like terms: 0 + 17 = 17
-1a = 17

Divide each side by '-1'.
a = -17

Simplifying
a = -17
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 = {-17, 3}