42r^2-204r+144=0

Solution for 42r^2-204r+144=0 equation:

Simplifying
42r2 + -204r + 144 = 0

Reorder the terms:
144 + -204r + 42r2 = 0

Solving
144 + -204r + 42r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(24 + -34r + 7r2) = 0

Factor a trinomial.
6((6 + -7r)(4 + -1r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(6 + -7r)' equal to zero and attempt to solve:

Simplifying
6 + -7r = 0

Solving
6 + -7r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7r = 0 + -6
-7r = 0 + -6

Combine like terms: 0 + -6 = -6
-7r = -6

Divide each side by '-7'.
r = 0.8571428571

Simplifying
r = 0.8571428571
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {0.8571428571, 4}