(r-5)(7r+2)=0

Solution for (r-5)(7r+2)=0 equation:

Simplifying
(r + -5)(7r + 2) = 0

Reorder the terms:
(-5 + r)(7r + 2) = 0

Reorder the terms:
(-5 + r)(2 + 7r) = 0

Multiply (-5 + r) * (2 + 7r)
(-5(2 + 7r) + r(2 + 7r)) = 0
((2 * -5 + 7r * -5) + r(2 + 7r)) = 0
((-10 + -35r) + r(2 + 7r)) = 0
(-10 + -35r + (2 * r + 7r * r)) = 0
(-10 + -35r + (2r + 7r2)) = 0

Combine like terms: -35r + 2r = -33r
(-10 + -33r + 7r2) = 0

Solving
-10 + -33r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-2 + -7r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-2 + -7r)' equal to zero and attempt to solve:

Simplifying
-2 + -7r = 0

Solving
-2 + -7r = 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 + -7r = 0 + 2

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

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

Divide each side by '-7'.
r = -0.2857142857

Simplifying
r = -0.2857142857
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-0.2857142857, 5}