h^4+12=7h^2

Solution for h^4+12=7h^2 equation:

Simplifying
h4 + 12 = 7h2

Reorder the terms:
12 + h4 = 7h2

Solving
12 + h4 = 7h2

Solving for variable 'h'.

Reorder the terms:
12 + -7h2 + h4 = 7h2 + -7h2

Combine like terms: 7h2 + -7h2 = 0
12 + -7h2 + h4 = 0

Factor a trinomial.
(3 + -1h2)(4 + -1h2) = 0

Factor a difference between two squares.
(3 + -1h2)((2 + h)(2 + -1h)) = 0

Subproblem 1
Set the factor '(3 + -1h2)' equal to zero and attempt to solve:

Simplifying
3 + -1h2 = 0

Solving
3 + -1h2 = 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 + -1h2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1h2 = 0 + -3
-1h2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1h2 = -3

Divide each side by '-1'.
h2 = 3

Simplifying
h2 = 3

Take the square root of each side:
h = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(2 + h)' equal to zero and attempt to solve:

Simplifying
2 + h = 0

Solving
2 + h = 0

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

Add '-2' to each side of the equation.
2 + -2 + h = 0 + -2

Combine like terms: 2 + -2 = 0
0 + h = 0 + -2
h = 0 + -2

Combine like terms: 0 + -2 = -2
h = -2

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

Simplifying
2 + -1h = 0

Solving
2 + -1h = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1h = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1h = 0 + -2
-1h = 0 + -2

Combine like terms: 0 + -2 = -2
-1h = -2

Divide each side by '-1'.
h = 2

Simplifying
h = 2
Solution
h = {-1.732050808, 1.732050808, -2, 2}