(4n+5)(3n-7)=0

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Solution for (4n+5)(3n-7)=0 equation:


Simplifying
(4n + 5)(3n + -7) = 0

Reorder the terms:
(5 + 4n)(3n + -7) = 0

Reorder the terms:
(5 + 4n)(-7 + 3n) = 0

Multiply (5 + 4n) * (-7 + 3n)
(5(-7 + 3n) + 4n * (-7 + 3n)) = 0
((-7 * 5 + 3n * 5) + 4n * (-7 + 3n)) = 0
((-35 + 15n) + 4n * (-7 + 3n)) = 0
(-35 + 15n + (-7 * 4n + 3n * 4n)) = 0
(-35 + 15n + (-28n + 12n2)) = 0

Combine like terms: 15n + -28n = -13n
(-35 + -13n + 12n2) = 0

Solving
-35 + -13n + 12n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -4n)(7 + -3n) = 0

Subproblem 1

Set the factor '(-5 + -4n)' equal to zero and attempt to solve: Simplifying -5 + -4n = 0 Solving -5 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4n = 0 + 5 -4n = 0 + 5 Combine like terms: 0 + 5 = 5 -4n = 5 Divide each side by '-4'. n = -1.25 Simplifying n = -1.25

Subproblem 2

Set the factor '(7 + -3n)' equal to zero and attempt to solve: Simplifying 7 + -3n = 0 Solving 7 + -3n = 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 + -3n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3n = 0 + -7 -3n = 0 + -7 Combine like terms: 0 + -7 = -7 -3n = -7 Divide each side by '-3'. n = 2.333333333 Simplifying n = 2.333333333

Solution

n = {-1.25, 2.333333333}

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