(2r-8)(3r+2)=0

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Solution for (2r-8)(3r+2)=0 equation: 


Simplifying
(2r + -8)(3r + 2) = 0

Reorder the terms:
(-8 + 2r)(3r + 2) = 0

Reorder the terms:
(-8 + 2r)(2 + 3r) = 0

Multiply (-8 + 2r) * (2 + 3r)
(-8(2 + 3r) + 2r * (2 + 3r)) = 0
((2 * -8 + 3r * -8) + 2r * (2 + 3r)) = 0
((-16 + -24r) + 2r * (2 + 3r)) = 0
(-16 + -24r + (2 * 2r + 3r * 2r)) = 0
(-16 + -24r + (4r + 6r2)) = 0

Combine like terms: -24r + 4r = -20r
(-16 + -20r + 6r2) = 0

Solving
-16 + -20r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -10r + 3r2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -3r)' equal to zero and attempt to solve:

Simplifying
-2 + -3r = 0

Solving
-2 + -3r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3r = 0 + 2
-3r = 0 + 2

Combine like terms: 0 + 2 = 2
-3r = 2

Divide each side by '-3'.
r = -0.6666666667

Simplifying
r = -0.6666666667

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 = {-0.6666666667, 4}

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