(7r+4)(2r-6)=

Solution for (7r+4)(2r-6)= equation:

Simplifying
(7r + 4)(2r + -6) = 0

Reorder the terms:
(4 + 7r)(2r + -6) = 0

Reorder the terms:
(4 + 7r)(-6 + 2r) = 0

Multiply (4 + 7r) * (-6 + 2r)
(4(-6 + 2r) + 7r * (-6 + 2r)) = 0
((-6 * 4 + 2r * 4) + 7r * (-6 + 2r)) = 0
((-24 + 8r) + 7r * (-6 + 2r)) = 0
(-24 + 8r + (-6 * 7r + 2r * 7r)) = 0
(-24 + 8r + (-42r + 14r2)) = 0

Combine like terms: 8r + -42r = -34r
(-24 + -34r + 14r2) = 0

Solving
-24 + -34r + 14r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -17r + 7r2) = 0

Factor a trinomial.
2((-4 + -7r)(3 + -1r)) = 0

Ignore the factor 2.
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}