42r^2-17r=15

Solution for 42r^2-17r=15 equation:

Simplifying
42r2 + -17r = 15

Reorder the terms:
-17r + 42r2 = 15

Solving
-17r + 42r2 = 15

Solving for variable 'r'.

Reorder the terms:
-15 + -17r + 42r2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -17r + 42r2 = 0

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

Subproblem 1
Set the factor '(-3 + -7r)' equal to zero and attempt to solve:

Simplifying
-3 + -7r = 0

Solving
-3 + -7r = 0

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

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

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

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

Divide each side by '-7'.
r = -0.4285714286

Simplifying
r = -0.4285714286
Subproblem 2
Set the factor '(5 + -6r)' equal to zero and attempt to solve:

Simplifying
5 + -6r = 0

Solving
5 + -6r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6r = 0 + -5
-6r = 0 + -5

Combine like terms: 0 + -5 = -5
-6r = -5

Divide each side by '-6'.
r = 0.8333333333

Simplifying
r = 0.8333333333
Solution
r = {-0.4285714286, 0.8333333333}