(3n+5)(4n+5)=

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Solution for (3n+5)(4n+5)= equation:


Simplifying
(3n + 5)(4n + 5) = 0

Reorder the terms:
(5 + 3n)(4n + 5) = 0

Reorder the terms:
(5 + 3n)(5 + 4n) = 0

Multiply (5 + 3n) * (5 + 4n)
(5(5 + 4n) + 3n * (5 + 4n)) = 0
((5 * 5 + 4n * 5) + 3n * (5 + 4n)) = 0
((25 + 20n) + 3n * (5 + 4n)) = 0
(25 + 20n + (5 * 3n + 4n * 3n)) = 0
(25 + 20n + (15n + 12n2)) = 0

Combine like terms: 20n + 15n = 35n
(25 + 35n + 12n2) = 0

Solving
25 + 35n + 12n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + 3n)(5 + 4n) = 0

Subproblem 1

Set the factor '(5 + 3n)' equal to zero and attempt to solve: Simplifying 5 + 3n = 0 Solving 5 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3n = 0 + -5 3n = 0 + -5 Combine like terms: 0 + -5 = -5 3n = -5 Divide each side by '3'. n = -1.666666667 Simplifying n = -1.666666667

Subproblem 2

Set the factor '(5 + 4n)' equal to zero and attempt to solve: Simplifying 5 + 4n = 0 Solving 5 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4n = 0 + -5 4n = 0 + -5 Combine like terms: 0 + -5 = -5 4n = -5 Divide each side by '4'. n = -1.25 Simplifying n = -1.25

Solution

n = {-1.666666667, -1.25}

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