r^4-144=0

Solution for r^4-144=0 equation:

Simplifying
r4 + -144 = 0

Reorder the terms:
-144 + r4 = 0

Solving
-144 + r4 = 0

Solving for variable 'r'.

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

Add '144' to each side of the equation.
-144 + 144 + r4 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + r4 = 0 + 144
r4 = 0 + 144

Combine like terms: 0 + 144 = 144
r4 = 144

Simplifying
r4 = 144

Reorder the terms:
-144 + r4 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + r4 = 0

Factor a difference between two squares.
(12 + r2)(-12 + r2) = 0

Subproblem 1
Set the factor '(12 + r2)' equal to zero and attempt to solve:

Simplifying
12 + r2 = 0

Solving
12 + r2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + r2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + r2 = 0 + -12
r2 = 0 + -12

Combine like terms: 0 + -12 = -12
r2 = -12

Simplifying
r2 = -12

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-12 + r2)' equal to zero and attempt to solve:

Simplifying
-12 + r2 = 0

Solving
-12 + r2 = 0

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

Add '12' to each side of the equation.
-12 + 12 + r2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + r2 = 0 + 12
r2 = 0 + 12

Combine like terms: 0 + 12 = 12
r2 = 12

Simplifying
r2 = 12

Take the square root of each side:
r = {-3.464101615, 3.464101615}
Solution
r = {-3.464101615, 3.464101615}