4n^2=35+4n

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Solution for 4n^2=35+4n equation:


Simplifying
4n2 = 35 + 4n

Solving
4n2 = 35 + 4n

Solving for variable 'n'.

Reorder the terms:
-35 + -4n + 4n2 = 35 + 4n + -35 + -4n

Reorder the terms:
-35 + -4n + 4n2 = 35 + -35 + 4n + -4n

Combine like terms: 35 + -35 = 0
-35 + -4n + 4n2 = 0 + 4n + -4n
-35 + -4n + 4n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
-35 + -4n + 4n2 = 0

Factor a trinomial.
(-5 + -2n)(7 + -2n) = 0

Subproblem 1

Set the factor '(-5 + -2n)' equal to zero and attempt to solve: Simplifying -5 + -2n = 0 Solving -5 + -2n = 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 + -2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2n = 0 + 5 -2n = 0 + 5 Combine like terms: 0 + 5 = 5 -2n = 5 Divide each side by '-2'. n = -2.5 Simplifying n = -2.5

Subproblem 2

Set the factor '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5

Solution

n = {-2.5, 3.5}

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