(7r+4)(3r-9)=0

Solution for (7r+4)(3r-9)=0 equation:

Simplifying
(7r + 4)(3r + -9) = 0

Reorder the terms:
(4 + 7r)(3r + -9) = 0

Reorder the terms:
(4 + 7r)(-9 + 3r) = 0

Multiply (4 + 7r) * (-9 + 3r)
(4(-9 + 3r) + 7r * (-9 + 3r)) = 0
((-9 * 4 + 3r * 4) + 7r * (-9 + 3r)) = 0
((-36 + 12r) + 7r * (-9 + 3r)) = 0
(-36 + 12r + (-9 * 7r + 3r * 7r)) = 0
(-36 + 12r + (-63r + 21r2)) = 0

Combine like terms: 12r + -63r = -51r
(-36 + -51r + 21r2) = 0

Solving
-36 + -51r + 21r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -17r + 7r2) = 0

Factor a trinomial.
3((-4 + -7r)(3 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -7r)' equal to zero and attempt to solve:

Simplifying
-4 + -7r = 0

Solving
-4 + -7r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7r = 0 + 4
-7r = 0 + 4

Combine like terms: 0 + 4 = 4
-7r = 4

Divide each side by '-7'.
r = -0.5714285714

Simplifying
r = -0.5714285714
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 = {-0.5714285714, 3}