9n^2=7n^2+3n

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Solution for 9n^2=7n^2+3n equation:


Simplifying
9n2 = 7n2 + 3n

Reorder the terms:
9n2 = 3n + 7n2

Solving
9n2 = 3n + 7n2

Solving for variable 'n'.

Reorder the terms:
-3n + 9n2 + -7n2 = 3n + 7n2 + -3n + -7n2

Combine like terms: 9n2 + -7n2 = 2n2
-3n + 2n2 = 3n + 7n2 + -3n + -7n2

Reorder the terms:
-3n + 2n2 = 3n + -3n + 7n2 + -7n2

Combine like terms: 3n + -3n = 0
-3n + 2n2 = 0 + 7n2 + -7n2
-3n + 2n2 = 7n2 + -7n2

Combine like terms: 7n2 + -7n2 = 0
-3n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3 + 2n) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(-3 + 2n)' equal to zero and attempt to solve: Simplifying -3 + 2n = 0 Solving -3 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2n = 0 + 3 2n = 0 + 3 Combine like terms: 0 + 3 = 3 2n = 3 Divide each side by '2'. n = 1.5 Simplifying n = 1.5

Solution

n = {0, 1.5}

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