(5r+7)(3r+5)=0

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Solution for (5r+7)(3r+5)=0 equation:


Simplifying
(5r + 7)(3r + 5) = 0

Reorder the terms:
(7 + 5r)(3r + 5) = 0

Reorder the terms:
(7 + 5r)(5 + 3r) = 0

Multiply (7 + 5r) * (5 + 3r)
(7(5 + 3r) + 5r * (5 + 3r)) = 0
((5 * 7 + 3r * 7) + 5r * (5 + 3r)) = 0
((35 + 21r) + 5r * (5 + 3r)) = 0
(35 + 21r + (5 * 5r + 3r * 5r)) = 0
(35 + 21r + (25r + 15r2)) = 0

Combine like terms: 21r + 25r = 46r
(35 + 46r + 15r2) = 0

Solving
35 + 46r + 15r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + 3r)(7 + 5r) = 0

Subproblem 1

Set the factor '(5 + 3r)' equal to zero and attempt to solve: Simplifying 5 + 3r = 0 Solving 5 + 3r = 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 + 3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3r = 0 + -5 3r = 0 + -5 Combine like terms: 0 + -5 = -5 3r = -5 Divide each side by '3'. r = -1.666666667 Simplifying r = -1.666666667

Subproblem 2

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

Solution

r = {-1.666666667, -1.4}

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