x^2+15x+51=1

Solution for x^2+15x+51=1 equation:

Simplifying
x2 + 15x + 51 = 1

Reorder the terms:
51 + 15x + x2 = 1

Solving
51 + 15x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
51 + -1 + 15x + x2 = 1 + -1

Combine like terms: 51 + -1 = 50
50 + 15x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
50 + 15x + x2 = 0

Factor a trinomial.
(10 + x)(5 + x) = 0

Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-10, -5}