10r^2+33r-7=0

Solution for 10r^2+33r-7=0 equation:

Simplifying
10r2 + 33r + -7 = 0

Reorder the terms:
-7 + 33r + 10r2 = 0

Solving
-7 + 33r + 10r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -2r)(1 + -5r) = 0

Subproblem 1
Set the factor '(-7 + -2r)' equal to zero and attempt to solve:

Simplifying
-7 + -2r = 0

Solving
-7 + -2r = 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 + -2r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2r = 0 + 7
-2r = 0 + 7

Combine like terms: 0 + 7 = 7
-2r = 7

Divide each side by '-2'.
r = -3.5

Simplifying
r = -3.5
Subproblem 2
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
Solution
r = {-3.5, 0.2}