(8r+5)(3r-8)=0

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Solution for (8r+5)(3r-8)=0 equation: 


Simplifying
(8r + 5)(3r + -8) = 0

Reorder the terms:
(5 + 8r)(3r + -8) = 0

Reorder the terms:
(5 + 8r)(-8 + 3r) = 0

Multiply (5 + 8r) * (-8 + 3r)
(5(-8 + 3r) + 8r * (-8 + 3r)) = 0
((-8 * 5 + 3r * 5) + 8r * (-8 + 3r)) = 0
((-40 + 15r) + 8r * (-8 + 3r)) = 0
(-40 + 15r + (-8 * 8r + 3r * 8r)) = 0
(-40 + 15r + (-64r + 24r2)) = 0

Combine like terms: 15r + -64r = -49r
(-40 + -49r + 24r2) = 0

Solving
-40 + -49r + 24r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -8r)(8 + -3r) = 0


Subproblem 1
Set the factor '(-5 + -8r)' equal to zero and attempt to solve:

Simplifying
-5 + -8r = 0

Solving
-5 + -8r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -8r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8r = 0 + 5
-8r = 0 + 5

Combine like terms: 0 + 5 = 5
-8r = 5

Divide each side by '-8'.
r = -0.625

Simplifying
r = -0.625

Subproblem 2
Set the factor '(8 + -3r)' equal to zero and attempt to solve:

Simplifying
8 + -3r = 0

Solving
8 + -3r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3r = 0 + -8
-3r = 0 + -8

Combine like terms: 0 + -8 = -8
-3r = -8

Divide each side by '-3'.
r = 2.666666667

Simplifying
r = 2.666666667
Solution
r = {-0.625, 2.666666667}

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