(4r-12)(7r-16)=0

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Solution for (4r-12)(7r-16)=0 equation: 


Simplifying
(4r + -12)(7r + -16) = 0

Reorder the terms:
(-12 + 4r)(7r + -16) = 0

Reorder the terms:
(-12 + 4r)(-16 + 7r) = 0

Multiply (-12 + 4r) * (-16 + 7r)
(-12(-16 + 7r) + 4r * (-16 + 7r)) = 0
((-16 * -12 + 7r * -12) + 4r * (-16 + 7r)) = 0
((192 + -84r) + 4r * (-16 + 7r)) = 0
(192 + -84r + (-16 * 4r + 7r * 4r)) = 0
(192 + -84r + (-64r + 28r2)) = 0

Combine like terms: -84r + -64r = -148r
(192 + -148r + 28r2) = 0

Solving
192 + -148r + 28r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(48 + -37r + 7r2) = 0

Factor a trinomial.
4((16 + -7r)(3 + -1r)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(16 + -7r)' equal to zero and attempt to solve:

Simplifying
16 + -7r = 0

Solving
16 + -7r = 0

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

Add '-16' to each side of the equation.
16 + -16 + -7r = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -7r = 0 + -16
-7r = 0 + -16

Combine like terms: 0 + -16 = -16
-7r = -16

Divide each side by '-7'.
r = 2.285714286

Simplifying
r = 2.285714286

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 = {2.285714286, 3}

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