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

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


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

Multiply (7 + -3r) * (8 + -2r)
(7(8 + -2r) + -3r * (8 + -2r)) = 0
((8 * 7 + -2r * 7) + -3r * (8 + -2r)) = 0
((56 + -14r) + -3r * (8 + -2r)) = 0
(56 + -14r + (8 * -3r + -2r * -3r)) = 0
(56 + -14r + (-24r + 6r2)) = 0

Combine like terms: -14r + -24r = -38r
(56 + -38r + 6r2) = 0

Solving
56 + -38r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -19r + 3r2) = 0

Factor a trinomial.
2((7 + -3r)(4 + -1r)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -3r)' equal to zero and attempt to solve:

Simplifying
7 + -3r = 0

Solving
7 + -3r = 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 + -3r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3r = 0 + -7
-3r = 0 + -7

Combine like terms: 0 + -7 = -7
-3r = -7

Divide each side by '-3'.
r = 2.333333333

Simplifying
r = 2.333333333

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 = {2.333333333, 4}

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