(n-4)(4n+2)=

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Solution for (n-4)(4n+2)= equation:


Simplifying
(n + -4)(4n + 2) = 0

Reorder the terms:
(-4 + n)(4n + 2) = 0

Reorder the terms:
(-4 + n)(2 + 4n) = 0

Multiply (-4 + n) * (2 + 4n)
(-4(2 + 4n) + n(2 + 4n)) = 0
((2 * -4 + 4n * -4) + n(2 + 4n)) = 0
((-8 + -16n) + n(2 + 4n)) = 0
(-8 + -16n + (2 * n + 4n * n)) = 0
(-8 + -16n + (2n + 4n2)) = 0

Combine like terms: -16n + 2n = -14n
(-8 + -14n + 4n2) = 0

Solving
-8 + -14n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -7n + 2n2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -2n)' equal to zero and attempt to solve: Simplifying -1 + -2n = 0 Solving -1 + -2n = 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 + -2n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2n = 0 + 1 -2n = 0 + 1 Combine like terms: 0 + 1 = 1 -2n = 1 Divide each side by '-2'. n = -0.5 Simplifying n = -0.5

Subproblem 2

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

Solution

n = {-0.5, 4}

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