(5r-8)(4r-7)=0

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Solution for (5r-8)(4r-7)=0 equation: 


Simplifying
(5r + -8)(4r + -7) = 0

Reorder the terms:
(-8 + 5r)(4r + -7) = 0

Reorder the terms:
(-8 + 5r)(-7 + 4r) = 0

Multiply (-8 + 5r) * (-7 + 4r)
(-8(-7 + 4r) + 5r * (-7 + 4r)) = 0
((-7 * -8 + 4r * -8) + 5r * (-7 + 4r)) = 0
((56 + -32r) + 5r * (-7 + 4r)) = 0
(56 + -32r + (-7 * 5r + 4r * 5r)) = 0
(56 + -32r + (-35r + 20r2)) = 0

Combine like terms: -32r + -35r = -67r
(56 + -67r + 20r2) = 0

Solving
56 + -67r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(8 + -5r)(7 + -4r) = 0


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

Simplifying
8 + -5r = 0

Solving
8 + -5r = 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 + -5r = 0 + -8

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

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

Divide each side by '-5'.
r = 1.6

Simplifying
r = 1.6

Subproblem 2
Set the factor '(7 + -4r)' equal to zero and attempt to solve:

Simplifying
7 + -4r = 0

Solving
7 + -4r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4r = 0 + -7
-4r = 0 + -7

Combine like terms: 0 + -7 = -7
-4r = -7

Divide each side by '-4'.
r = 1.75

Simplifying
r = 1.75
Solution
r = {1.6, 1.75}

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