a^2+10a-51=5

Solution for a^2+10a-51=5 equation:

Simplifying
a2 + 10a + -51 = 5

Reorder the terms:
-51 + 10a + a2 = 5

Solving
-51 + 10a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
-51 + -5 + 10a + a2 = 5 + -5

Combine like terms: -51 + -5 = -56
-56 + 10a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-56 + 10a + a2 = 0

Factor a trinomial.
(-14 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-14 + -1a)' equal to zero and attempt to solve:

Simplifying
-14 + -1a = 0

Solving
-14 + -1a = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1a = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1a = 0 + 14
-1a = 0 + 14

Combine like terms: 0 + 14 = 14
-1a = 14

Divide each side by '-1'.
a = -14

Simplifying
a = -14
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 = {-14, 4}