2x=-x^2+x+42

Solution for 2x=-x^2+x+42 equation:

Simplifying
2x = -1x2 + x + 42

Reorder the terms:
2x = 42 + x + -1x2

Solving
2x = 42 + x + -1x2

Solving for variable 'x'.

Reorder the terms:
-42 + 2x + -1x + x2 = 42 + x + -1x2 + -42 + -1x + x2

Combine like terms: 2x + -1x = 1x
-42 + 1x + x2 = 42 + x + -1x2 + -42 + -1x + x2

Reorder the terms:
-42 + 1x + x2 = 42 + -42 + x + -1x + -1x2 + x2

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

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

Combine like terms: -1x2 + x2 = 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}