10n^2-7=5n^2-2n

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Solution for 10n^2-7=5n^2-2n equation:


Simplifying
10n2 + -7 = 5n2 + -2n

Reorder the terms:
-7 + 10n2 = 5n2 + -2n

Reorder the terms:
-7 + 10n2 = -2n + 5n2

Solving
-7 + 10n2 = -2n + 5n2

Solving for variable 'n'.

Reorder the terms:
-7 + 2n + 10n2 + -5n2 = -2n + 5n2 + 2n + -5n2

Combine like terms: 10n2 + -5n2 = 5n2
-7 + 2n + 5n2 = -2n + 5n2 + 2n + -5n2

Reorder the terms:
-7 + 2n + 5n2 = -2n + 2n + 5n2 + -5n2

Combine like terms: -2n + 2n = 0
-7 + 2n + 5n2 = 0 + 5n2 + -5n2
-7 + 2n + 5n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
-7 + 2n + 5n2 = 0

Factor a trinomial.
(-7 + -5n)(1 + -1n) = 0

Subproblem 1

Set the factor '(-7 + -5n)' equal to zero and attempt to solve: Simplifying -7 + -5n = 0 Solving -7 + -5n = 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 + -5n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5n = 0 + 7 -5n = 0 + 7 Combine like terms: 0 + 7 = 7 -5n = 7 Divide each side by '-5'. n = -1.4 Simplifying n = -1.4

Subproblem 2

Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1

Solution

n = {-1.4, 1}

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