(3r-8)(2r-7)=0

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Solution for (3r-8)(2r-7)=0 equation: 


Simplifying
(3r + -8)(2r + -7) = 0

Reorder the terms:
(-8 + 3r)(2r + -7) = 0

Reorder the terms:
(-8 + 3r)(-7 + 2r) = 0

Multiply (-8 + 3r) * (-7 + 2r)
(-8(-7 + 2r) + 3r * (-7 + 2r)) = 0
((-7 * -8 + 2r * -8) + 3r * (-7 + 2r)) = 0
((56 + -16r) + 3r * (-7 + 2r)) = 0
(56 + -16r + (-7 * 3r + 2r * 3r)) = 0
(56 + -16r + (-21r + 6r2)) = 0

Combine like terms: -16r + -21r = -37r
(56 + -37r + 6r2) = 0

Solving
56 + -37r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(8 + -3r)(7 + -2r) = 0


Subproblem 1
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

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

Simplifying
7 + -2r = 0

Solving
7 + -2r = 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 + -2r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2r = 0 + -7
-2r = 0 + -7

Combine like terms: 0 + -7 = -7
-2r = -7

Divide each side by '-2'.
r = 3.5

Simplifying
r = 3.5
Solution
r = {2.666666667, 3.5}

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