4n^2=25+15n

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Solution for 4n^2=25+15n equation:


Simplifying
4n2 = 25 + 15n

Solving
4n2 = 25 + 15n

Solving for variable 'n'.

Reorder the terms:
-25 + -15n + 4n2 = 25 + 15n + -25 + -15n

Reorder the terms:
-25 + -15n + 4n2 = 25 + -25 + 15n + -15n

Combine like terms: 25 + -25 = 0
-25 + -15n + 4n2 = 0 + 15n + -15n
-25 + -15n + 4n2 = 15n + -15n

Combine like terms: 15n + -15n = 0
-25 + -15n + 4n2 = 0

Factor a trinomial.
(-5 + -4n)(5 + -1n) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5

Solution

n = {-1.25, 5}

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