-2r^2-7r=6

Solution for -2r^2-7r=6 equation:

Simplifying
-2r2 + -7r = 6

Reorder the terms:
-7r + -2r2 = 6

Solving
-7r + -2r2 = 6

Solving for variable 'r'.

Reorder the terms:
-6 + -7r + -2r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -7r + -2r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 7r + 2r2) = 0

Factor a trinomial.
-1((2 + r)(3 + 2r)) = 0

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

Simplifying
2 + r = 0

Solving
2 + r = 0

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

Add '-2' to each side of the equation.
2 + -2 + r = 0 + -2

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

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

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

Simplifying
3 + 2r = 0

Solving
3 + 2r = 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 + 2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2r = 0 + -3
2r = 0 + -3

Combine like terms: 0 + -3 = -3
2r = -3

Divide each side by '2'.
r = -1.5

Simplifying
r = -1.5
Solution
r = {-2, -1.5}