(9r+7)(2r-6)=0

Solution for (9r+7)(2r-6)=0 equation:

Simplifying
(9r + 7)(2r + -6) = 0

Reorder the terms:
(7 + 9r)(2r + -6) = 0

Reorder the terms:
(7 + 9r)(-6 + 2r) = 0

Multiply (7 + 9r) * (-6 + 2r)
(7(-6 + 2r) + 9r * (-6 + 2r)) = 0
((-6 * 7 + 2r * 7) + 9r * (-6 + 2r)) = 0
((-42 + 14r) + 9r * (-6 + 2r)) = 0
(-42 + 14r + (-6 * 9r + 2r * 9r)) = 0
(-42 + 14r + (-54r + 18r2)) = 0

Combine like terms: 14r + -54r = -40r
(-42 + -40r + 18r2) = 0

Solving
-42 + -40r + 18r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -20r + 9r2) = 0

Factor a trinomial.
2((-7 + -9r)(3 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -9r)' equal to zero and attempt to solve:

Simplifying
-7 + -9r = 0

Solving
-7 + -9r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -9r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -9r = 0 + 7
-9r = 0 + 7

Combine like terms: 0 + 7 = 7
-9r = 7

Divide each side by '-9'.
r = -0.7777777778

Simplifying
r = -0.7777777778
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 = {-0.7777777778, 3}