x(9-x)+2=-34

Solution for x(9-x)+2=-34 equation:

Simplifying
x(9 + -1x) + 2 = -34
(9 * x + -1x * x) + 2 = -34
(9x + -1x2) + 2 = -34

Reorder the terms:
2 + 9x + -1x2 = -34

Solving
2 + 9x + -1x2 = -34

Solving for variable 'x'.

Reorder the terms:
2 + 34 + 9x + -1x2 = -34 + 34

Combine like terms: 2 + 34 = 36
36 + 9x + -1x2 = -34 + 34

Combine like terms: -34 + 34 = 0
36 + 9x + -1x2 = 0

Factor a trinomial.
(12 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {12, -3}