7r^2+12r-90=9

Solution for 7r^2+12r-90=9 equation:

Simplifying
7r2 + 12r + -90 = 9

Reorder the terms:
-90 + 12r + 7r2 = 9

Solving
-90 + 12r + 7r2 = 9

Solving for variable 'r'.

Reorder the terms:
-90 + -9 + 12r + 7r2 = 9 + -9

Combine like terms: -90 + -9 = -99
-99 + 12r + 7r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-99 + 12r + 7r2 = 0

Factor a trinomial.
(-33 + -7r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-33 + -7r)' equal to zero and attempt to solve:

Simplifying
-33 + -7r = 0

Solving
-33 + -7r = 0

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

Add '33' to each side of the equation.
-33 + 33 + -7r = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -7r = 0 + 33
-7r = 0 + 33

Combine like terms: 0 + 33 = 33
-7r = 33

Divide each side by '-7'.
r = -4.714285714

Simplifying
r = -4.714285714
Subproblem 2
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
Solution
r = {-4.714285714, 3}