20n^2+32n=16

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Solution for 20n^2+32n=16 equation:


Simplifying
20n2 + 32n = 16

Reorder the terms:
32n + 20n2 = 16

Solving
32n + 20n2 = 16

Solving for variable 'n'.

Reorder the terms:
-16 + 32n + 20n2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 32n + 20n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 8n + 5n2) = 0

Factor a trinomial.
4((-2 + -1n)(2 + -5n)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2

Subproblem 2

Set the factor '(2 + -5n)' equal to zero and attempt to solve: Simplifying 2 + -5n = 0 Solving 2 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n = 0 + -2 -5n = 0 + -2 Combine like terms: 0 + -2 = -2 -5n = -2 Divide each side by '-5'. n = 0.4 Simplifying n = 0.4

Solution

n = {-2, 0.4}

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