7r^2+38r-24=0

Solution for 7r^2+38r-24=0 equation:

Simplifying
7r2 + 38r + -24 = 0

Reorder the terms:
-24 + 38r + 7r2 = 0

Solving
-24 + 38r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -1r)(4 + -7r) = 0

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

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
Subproblem 2
Set the factor '(4 + -7r)' equal to zero and attempt to solve:

Simplifying
4 + -7r = 0

Solving
4 + -7r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7r = 0 + -4
-7r = 0 + -4

Combine like terms: 0 + -4 = -4
-7r = -4

Divide each side by '-7'.
r = 0.5714285714

Simplifying
r = 0.5714285714
Solution
r = {-6, 0.5714285714}