(11r+7)(4r-7)=0

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Solution for (11r+7)(4r-7)=0 equation: 


Simplifying
(11r + 7)(4r + -7) = 0

Reorder the terms:
(7 + 11r)(4r + -7) = 0

Reorder the terms:
(7 + 11r)(-7 + 4r) = 0

Multiply (7 + 11r) * (-7 + 4r)
(7(-7 + 4r) + 11r * (-7 + 4r)) = 0
((-7 * 7 + 4r * 7) + 11r * (-7 + 4r)) = 0
((-49 + 28r) + 11r * (-7 + 4r)) = 0
(-49 + 28r + (-7 * 11r + 4r * 11r)) = 0
(-49 + 28r + (-77r + 44r2)) = 0

Combine like terms: 28r + -77r = -49r
(-49 + -49r + 44r2) = 0

Solving
-49 + -49r + 44r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -11r)(7 + -4r) = 0


Subproblem 1
Set the factor '(-7 + -11r)' equal to zero and attempt to solve:

Simplifying
-7 + -11r = 0

Solving
-7 + -11r = 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 + -11r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -11r = 0 + 7
-11r = 0 + 7

Combine like terms: 0 + 7 = 7
-11r = 7

Divide each side by '-11'.
r = -0.6363636364

Simplifying
r = -0.6363636364

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 = {-0.6363636364, 1.75}

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