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

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


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

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

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

Multiply (-7 + 4r) * (-4 + 7r)
(-7(-4 + 7r) + 4r * (-4 + 7r)) = 0
((-4 * -7 + 7r * -7) + 4r * (-4 + 7r)) = 0
((28 + -49r) + 4r * (-4 + 7r)) = 0
(28 + -49r + (-4 * 4r + 7r * 4r)) = 0
(28 + -49r + (-16r + 28r2)) = 0

Combine like terms: -49r + -16r = -65r
(28 + -65r + 28r2) = 0

Solving
28 + -65r + 28r2 = 0

Solving for variable 'r'.

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


Subproblem 1
Set the factor '(4 + -7r)' equal to zero and attempt to solve:

Simplifying
4 + -7r = 0

Solving
4 + -7r = 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 + -7r = 0 + -4

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

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

Divide each side by '-7'.
r = 0.5714285714

Simplifying
r = 0.5714285714

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 = {0.5714285714, 1.75}

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