(x+41)*x=282

Solution for (x+41)*x=282 equation:

Simplifying
(x + 41) * x = 282

Reorder the terms:
(41 + x) * x = 282

Reorder the terms for easier multiplication:
x(41 + x) = 282
(41 * x + x * x) = 282
(41x + x2) = 282

Solving
41x + x2 = 282

Solving for variable 'x'.

Reorder the terms:
-282 + 41x + x2 = 282 + -282

Combine like terms: 282 + -282 = 0
-282 + 41x + x2 = 0

Factor a trinomial.
(-47 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-47 + -1x)' equal to zero and attempt to solve:

Simplifying
-47 + -1x = 0

Solving
-47 + -1x = 0

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

Add '47' to each side of the equation.
-47 + 47 + -1x = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -1x = 0 + 47
-1x = 0 + 47

Combine like terms: 0 + 47 = 47
-1x = 47

Divide each side by '-1'.
x = -47

Simplifying
x = -47
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 = {-47, 6}