h^2-42=-h

Solution for h^2-42=-h equation:

Simplifying
h2 + -42 = -1h

Reorder the terms:
-42 + h2 = -1h

Solving
-42 + h2 = -1h

Solving for variable 'h'.

Reorder the terms:
-42 + h + h2 = -1h + h

Combine like terms: -1h + h = 0
-42 + h + h2 = 0

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

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

Simplifying
-7 + -1h = 0

Solving
-7 + -1h = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1h = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1h = 0 + 7
-1h = 0 + 7

Combine like terms: 0 + 7 = 7
-1h = 7

Divide each side by '-1'.
h = -7

Simplifying
h = -7
Subproblem 2
Set the factor '(6 + -1h)' equal to zero and attempt to solve:

Simplifying
6 + -1h = 0

Solving
6 + -1h = 0

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

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

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

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

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

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