7r^2+19r-30=5r-9

Solution for 7r^2+19r-30=5r-9 equation:

Simplifying
7r2 + 19r + -30 = 5r + -9

Reorder the terms:
-30 + 19r + 7r2 = 5r + -9

Reorder the terms:
-30 + 19r + 7r2 = -9 + 5r

Solving
-30 + 19r + 7r2 = -9 + 5r

Solving for variable 'r'.

Reorder the terms:
-30 + 9 + 19r + -5r + 7r2 = -9 + 5r + 9 + -5r

Combine like terms: -30 + 9 = -21
-21 + 19r + -5r + 7r2 = -9 + 5r + 9 + -5r

Combine like terms: 19r + -5r = 14r
-21 + 14r + 7r2 = -9 + 5r + 9 + -5r

Reorder the terms:
-21 + 14r + 7r2 = -9 + 9 + 5r + -5r

Combine like terms: -9 + 9 = 0
-21 + 14r + 7r2 = 0 + 5r + -5r
-21 + 14r + 7r2 = 5r + -5r

Combine like terms: 5r + -5r = 0
-21 + 14r + 7r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + 2r + r2) = 0

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

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

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 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 + -1r = 0 + -1

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

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

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

Simplifying
r = 1
Solution
r = {-3, 1}