(2r-8)(4r-7)=0

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Solution for (2r-8)(4r-7)=0 equation: 


Simplifying
(2r + -8)(4r + -7) = 0

Reorder the terms:
(-8 + 2r)(4r + -7) = 0

Reorder the terms:
(-8 + 2r)(-7 + 4r) = 0

Multiply (-8 + 2r) * (-7 + 4r)
(-8(-7 + 4r) + 2r * (-7 + 4r)) = 0
((-7 * -8 + 4r * -8) + 2r * (-7 + 4r)) = 0
((56 + -32r) + 2r * (-7 + 4r)) = 0
(56 + -32r + (-7 * 2r + 4r * 2r)) = 0
(56 + -32r + (-14r + 8r2)) = 0

Combine like terms: -32r + -14r = -46r
(56 + -46r + 8r2) = 0

Solving
56 + -46r + 8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -23r + 4r2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {1.75, 4}

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