-4h^2+h+9=6

Solution for -4h^2+h+9=6 equation:

Simplifying
-4h2 + h + 9 = 6

Reorder the terms:
9 + h + -4h2 = 6

Solving
9 + h + -4h2 = 6

Solving for variable 'h'.

Reorder the terms:
9 + -6 + h + -4h2 = 6 + -6

Combine like terms: 9 + -6 = 3
3 + h + -4h2 = 6 + -6

Combine like terms: 6 + -6 = 0
3 + h + -4h2 = 0

Factor a trinomial.
(1 + -1h)(3 + 4h) = 0

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

Simplifying
1 + -1h = 0

Solving
1 + -1h = 0

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

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

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

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

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

Simplifying
h = 1
Subproblem 2
Set the factor '(3 + 4h)' equal to zero and attempt to solve:

Simplifying
3 + 4h = 0

Solving
3 + 4h = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4h = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4h = 0 + -3
4h = 0 + -3

Combine like terms: 0 + -3 = -3
4h = -3

Divide each side by '4'.
h = -0.75

Simplifying
h = -0.75
Solution
h = {1, -0.75}