(13r+8)(5r-15)=0

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Solution for (13r+8)(5r-15)=0 equation: 


Simplifying
(13r + 8)(5r + -15) = 0

Reorder the terms:
(8 + 13r)(5r + -15) = 0

Reorder the terms:
(8 + 13r)(-15 + 5r) = 0

Multiply (8 + 13r) * (-15 + 5r)
(8(-15 + 5r) + 13r * (-15 + 5r)) = 0
((-15 * 8 + 5r * 8) + 13r * (-15 + 5r)) = 0
((-120 + 40r) + 13r * (-15 + 5r)) = 0
(-120 + 40r + (-15 * 13r + 5r * 13r)) = 0
(-120 + 40r + (-195r + 65r2)) = 0

Combine like terms: 40r + -195r = -155r
(-120 + -155r + 65r2) = 0

Solving
-120 + -155r + 65r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + -31r + 13r2) = 0

Factor a trinomial.
5((-8 + -13r)(3 + -1r)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-8 + -13r)' equal to zero and attempt to solve:

Simplifying
-8 + -13r = 0

Solving
-8 + -13r = 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 + -13r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -13r = 0 + 8
-13r = 0 + 8

Combine like terms: 0 + 8 = 8
-13r = 8

Divide each side by '-13'.
r = -0.6153846154

Simplifying
r = -0.6153846154

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 = {-0.6153846154, 3}

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