90r^2-192r-42=0

Solution for 90r^2-192r-42=0 equation:

Simplifying
90r2 + -192r + -42 = 0

Reorder the terms:
-42 + -192r + 90r2 = 0

Solving
-42 + -192r + 90r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -32r + 15r2) = 0

Factor a trinomial.
6((-1 + -5r)(7 + -3r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -5r)' equal to zero and attempt to solve:

Simplifying
-1 + -5r = 0

Solving
-1 + -5r = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5r = 0 + 1
-5r = 0 + 1

Combine like terms: 0 + 1 = 1
-5r = 1

Divide each side by '-5'.
r = -0.2

Simplifying
r = -0.2
Subproblem 2
Set the factor '(7 + -3r)' equal to zero and attempt to solve:

Simplifying
7 + -3r = 0

Solving
7 + -3r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3r = 0 + -7
-3r = 0 + -7

Combine like terms: 0 + -7 = -7
-3r = -7

Divide each side by '-3'.
r = 2.333333333

Simplifying
r = 2.333333333
Solution
r = {-0.2, 2.333333333}