7r^2+43r+40=0

Solution for 7r^2+43r+40=0 equation:

Simplifying
7r2 + 43r + 40 = 0

Reorder the terms:
40 + 43r + 7r2 = 0

Solving
40 + 43r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + r)(8 + 7r) = 0

Subproblem 1
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 0

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

Add '-5' to each side of the equation.
5 + -5 + r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(8 + 7r)' equal to zero and attempt to solve:

Simplifying
8 + 7r = 0

Solving
8 + 7r = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7r = 0 + -8
7r = 0 + -8

Combine like terms: 0 + -8 = -8
7r = -8

Divide each side by '7'.
r = -1.142857143

Simplifying
r = -1.142857143
Solution
r = {-5, -1.142857143}