42=a(a+1)

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

Simplifying
42 = a(a + 1)

Reorder the terms:
42 = a(1 + a)
42 = (1 * a + a * a)
42 = (1a + a2)

Solving
42 = 1a + a2

Solving for variable 'a'.

Reorder the terms:
42 + -1a + -1a2 = 1a + -1a + a2 + -1a2

Combine like terms: 1a + -1a = 0
42 + -1a + -1a2 = 0 + a2 + -1a2
42 + -1a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
42 + -1a + -1a2 = 0

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

Subproblem 1
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

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

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

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

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

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

Simplifying
7 + a = 0

Solving
7 + a = 0

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

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

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

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

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