(7r+5)(2r-6)=0

Solution for (7r+5)(2r-6)=0 equation:

Simplifying
(7r + 5)(2r + -6) = 0

Reorder the terms:
(5 + 7r)(2r + -6) = 0

Reorder the terms:
(5 + 7r)(-6 + 2r) = 0

Multiply (5 + 7r) * (-6 + 2r)
(5(-6 + 2r) + 7r * (-6 + 2r)) = 0
((-6 * 5 + 2r * 5) + 7r * (-6 + 2r)) = 0
((-30 + 10r) + 7r * (-6 + 2r)) = 0
(-30 + 10r + (-6 * 7r + 2r * 7r)) = 0
(-30 + 10r + (-42r + 14r2)) = 0

Combine like terms: 10r + -42r = -32r
(-30 + -32r + 14r2) = 0

Solving
-30 + -32r + 14r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -16r + 7r2) = 0

Factor a trinomial.
2((-5 + -7r)(3 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -7r)' equal to zero and attempt to solve:

Simplifying
-5 + -7r = 0

Solving
-5 + -7r = 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 + -7r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7r = 0 + 5
-7r = 0 + 5

Combine like terms: 0 + 5 = 5
-7r = 5

Divide each side by '-7'.
r = -0.7142857143

Simplifying
r = -0.7142857143
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 = {-0.7142857143, 3}