4n^2=32n-28

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Solution for 4n^2=32n-28 equation:


Simplifying
4n2 = 32n + -28

Reorder the terms:
4n2 = -28 + 32n

Solving
4n2 = -28 + 32n

Solving for variable 'n'.

Reorder the terms:
28 + -32n + 4n2 = -28 + 32n + 28 + -32n

Reorder the terms:
28 + -32n + 4n2 = -28 + 28 + 32n + -32n

Combine like terms: -28 + 28 = 0
28 + -32n + 4n2 = 0 + 32n + -32n
28 + -32n + 4n2 = 32n + -32n

Combine like terms: 32n + -32n = 0
28 + -32n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -8n + n2) = 0

Factor a trinomial.
4((1 + -1n)(7 + -1n)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7

Solution

n = {1, 7}

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