2n^2-10n=7n-36

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Solution for 2n^2-10n=7n-36 equation:


Simplifying
2n2 + -10n = 7n + -36

Reorder the terms:
-10n + 2n2 = 7n + -36

Reorder the terms:
-10n + 2n2 = -36 + 7n

Solving
-10n + 2n2 = -36 + 7n

Solving for variable 'n'.

Reorder the terms:
36 + -10n + -7n + 2n2 = -36 + 7n + 36 + -7n

Combine like terms: -10n + -7n = -17n
36 + -17n + 2n2 = -36 + 7n + 36 + -7n

Reorder the terms:
36 + -17n + 2n2 = -36 + 36 + 7n + -7n

Combine like terms: -36 + 36 = 0
36 + -17n + 2n2 = 0 + 7n + -7n
36 + -17n + 2n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
36 + -17n + 2n2 = 0

Factor a trinomial.
(4 + -1n)(9 + -2n) = 0

Subproblem 1

Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 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 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4

Subproblem 2

Set the factor '(9 + -2n)' equal to zero and attempt to solve: Simplifying 9 + -2n = 0 Solving 9 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2n = 0 + -9 -2n = 0 + -9 Combine like terms: 0 + -9 = -9 -2n = -9 Divide each side by '-2'. n = 4.5 Simplifying n = 4.5

Solution

n = {4, 4.5}

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