x(x+1)-17=25

Solution for x(x+1)-17=25 equation:

Simplifying
x(x + 1) + -17 = 25

Reorder the terms:
x(1 + x) + -17 = 25
(1 * x + x * x) + -17 = 25
(1x + x2) + -17 = 25

Reorder the terms:
-17 + 1x + x2 = 25

Solving
-17 + 1x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
-17 + -25 + 1x + x2 = 25 + -25

Combine like terms: -17 + -25 = -42
-42 + 1x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-42 + 1x + x2 = 0

Factor a trinomial.
(-7 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

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

Simplifying
x = 6
Solution
x = {-7, 6}