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

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


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

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

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

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

Combine like terms: 4n + 25n = 29n
3(20 + 29n + 5n2) = 0
(20 * 3 + 29n * 3 + 5n2 * 3) = 0
(60 + 87n + 15n2) = 0

Solving
60 + 87n + 15n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + 29n + 5n2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5

Subproblem 2

Set the factor '(4 + 5n)' equal to zero and attempt to solve: Simplifying 4 + 5n = 0 Solving 4 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5n = 0 + -4 5n = 0 + -4 Combine like terms: 0 + -4 = -4 5n = -4 Divide each side by '5'. n = -0.8 Simplifying n = -0.8

Solution

n = {-5, -0.8}

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