7(4n-1)(2n+11)=0

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Solution for 7(4n-1)(2n+11)=0 equation:


Simplifying
7(4n + -1)(2n + 11) = 0

Reorder the terms:
7(-1 + 4n)(2n + 11) = 0

Reorder the terms:
7(-1 + 4n)(11 + 2n) = 0

Multiply (-1 + 4n) * (11 + 2n)
7(-1(11 + 2n) + 4n * (11 + 2n)) = 0
7((11 * -1 + 2n * -1) + 4n * (11 + 2n)) = 0
7((-11 + -2n) + 4n * (11 + 2n)) = 0
7(-11 + -2n + (11 * 4n + 2n * 4n)) = 0
7(-11 + -2n + (44n + 8n2)) = 0

Combine like terms: -2n + 44n = 42n
7(-11 + 42n + 8n2) = 0
(-11 * 7 + 42n * 7 + 8n2 * 7) = 0
(-77 + 294n + 56n2) = 0

Solving
-77 + 294n + 56n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-11 + 42n + 8n2) = 0

Factor a trinomial.
7((-11 + -2n)(1 + -4n)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-11 + -2n)' equal to zero and attempt to solve: Simplifying -11 + -2n = 0 Solving -11 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2n = 0 + 11 -2n = 0 + 11 Combine like terms: 0 + 11 = 11 -2n = 11 Divide each side by '-2'. n = -5.5 Simplifying n = -5.5

Subproblem 2

Set the factor '(1 + -4n)' equal to zero and attempt to solve: Simplifying 1 + -4n = 0 Solving 1 + -4n = 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 + -4n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4n = 0 + -1 -4n = 0 + -1 Combine like terms: 0 + -1 = -1 -4n = -1 Divide each side by '-4'. n = 0.25 Simplifying n = 0.25

Solution

n = {-5.5, 0.25}

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