(5r+6)(r-4)=0

Solution for (5r+6)(r-4)=0 equation:

Simplifying
(5r + 6)(r + -4) = 0

Reorder the terms:
(6 + 5r)(r + -4) = 0

Reorder the terms:
(6 + 5r)(-4 + r) = 0

Multiply (6 + 5r) * (-4 + r)
(6(-4 + r) + 5r * (-4 + r)) = 0
((-4 * 6 + r * 6) + 5r * (-4 + r)) = 0
((-24 + 6r) + 5r * (-4 + r)) = 0
(-24 + 6r + (-4 * 5r + r * 5r)) = 0
(-24 + 6r + (-20r + 5r2)) = 0

Combine like terms: 6r + -20r = -14r
(-24 + -14r + 5r2) = 0

Solving
-24 + -14r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -5r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-6 + -5r)' equal to zero and attempt to solve:

Simplifying
-6 + -5r = 0

Solving
-6 + -5r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5r = 0 + 6
-5r = 0 + 6

Combine like terms: 0 + 6 = 6
-5r = 6

Divide each side by '-5'.
r = -1.2

Simplifying
r = -1.2
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 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 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {-1.2, 4}