(n+7)(3n-4)=0

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Solution for (n+7)(3n-4)=0 equation:


Simplifying
(n + 7)(3n + -4) = 0

Reorder the terms:
(7 + n)(3n + -4) = 0

Reorder the terms:
(7 + n)(-4 + 3n) = 0

Multiply (7 + n) * (-4 + 3n)
(7(-4 + 3n) + n(-4 + 3n)) = 0
((-4 * 7 + 3n * 7) + n(-4 + 3n)) = 0
((-28 + 21n) + n(-4 + 3n)) = 0
(-28 + 21n + (-4 * n + 3n * n)) = 0
(-28 + 21n + (-4n + 3n2)) = 0

Combine like terms: 21n + -4n = 17n
(-28 + 17n + 3n2) = 0

Solving
-28 + 17n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -1n)(4 + -3n) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 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 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333

Solution

n = {-7, 1.333333333}

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