42=x(x+1)

Solution for 42=x(x+1) equation:

Simplifying
42 = x(x + 1)

Reorder the terms:
42 = x(1 + x)
42 = (1 * x + x * x)
42 = (1x + x2)

Solving
42 = 1x + x2

Solving for variable 'x'.

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

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

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

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

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

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

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