(4n-7)(-2n+5)=0

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Solution for (4n-7)(-2n+5)=0 equation:


Simplifying
(4n + -7)(-2n + 5) = 0

Reorder the terms:
(-7 + 4n)(-2n + 5) = 0

Reorder the terms:
(-7 + 4n)(5 + -2n) = 0

Multiply (-7 + 4n) * (5 + -2n)
(-7(5 + -2n) + 4n * (5 + -2n)) = 0
((5 * -7 + -2n * -7) + 4n * (5 + -2n)) = 0
((-35 + 14n) + 4n * (5 + -2n)) = 0
(-35 + 14n + (5 * 4n + -2n * 4n)) = 0
(-35 + 14n + (20n + -8n2)) = 0

Combine like terms: 14n + 20n = 34n
(-35 + 34n + -8n2) = 0

Solving
-35 + 34n + -8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + 2n)(7 + -4n) = 0

Subproblem 1

Set the factor '(-5 + 2n)' equal to zero and attempt to solve: Simplifying -5 + 2n = 0 Solving -5 + 2n = 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 + 2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2n = 0 + 5 2n = 0 + 5 Combine like terms: 0 + 5 = 5 2n = 5 Divide each side by '2'. n = 2.5 Simplifying n = 2.5

Subproblem 2

Set the factor '(7 + -4n)' equal to zero and attempt to solve: Simplifying 7 + -4n = 0 Solving 7 + -4n = 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 + -4n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4n = 0 + -7 -4n = 0 + -7 Combine like terms: 0 + -7 = -7 -4n = -7 Divide each side by '-4'. n = 1.75 Simplifying n = 1.75

Solution

n = {2.5, 1.75}

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