(5r+7)(6r+5)=0

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Solution for (5r+7)(6r+5)=0 equation: 


Simplifying
(5r + 7)(6r + 5) = 0

Reorder the terms:
(7 + 5r)(6r + 5) = 0

Reorder the terms:
(7 + 5r)(5 + 6r) = 0

Multiply (7 + 5r) * (5 + 6r)
(7(5 + 6r) + 5r * (5 + 6r)) = 0
((5 * 7 + 6r * 7) + 5r * (5 + 6r)) = 0
((35 + 42r) + 5r * (5 + 6r)) = 0
(35 + 42r + (5 * 5r + 6r * 5r)) = 0
(35 + 42r + (25r + 30r2)) = 0

Combine like terms: 42r + 25r = 67r
(35 + 67r + 30r2) = 0

Solving
35 + 67r + 30r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(7 + 5r)(5 + 6r) = 0


Subproblem 1
Set the factor '(7 + 5r)' equal to zero and attempt to solve:

Simplifying
7 + 5r = 0

Solving
7 + 5r = 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 + 5r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5r = 0 + -7
5r = 0 + -7

Combine like terms: 0 + -7 = -7
5r = -7

Divide each side by '5'.
r = -1.4

Simplifying
r = -1.4

Subproblem 2
Set the factor '(5 + 6r)' equal to zero and attempt to solve:

Simplifying
5 + 6r = 0

Solving
5 + 6r = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6r = 0 + -5
6r = 0 + -5

Combine like terms: 0 + -5 = -5
6r = -5

Divide each side by '6'.
r = -0.8333333333

Simplifying
r = -0.8333333333
Solution
r = {-1.4, -0.8333333333}

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