(5n+2)(3n-7)=0

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Solution for (5n+2)(3n-7)=0 equation: 


Simplifying
(5n + 2)(3n + -7) = 0

Reorder the terms:
(2 + 5n)(3n + -7) = 0

Reorder the terms:
(2 + 5n)(-7 + 3n) = 0

Multiply (2 + 5n) * (-7 + 3n)
(2(-7 + 3n) + 5n * (-7 + 3n)) = 0
((-7 * 2 + 3n * 2) + 5n * (-7 + 3n)) = 0
((-14 + 6n) + 5n * (-7 + 3n)) = 0
(-14 + 6n + (-7 * 5n + 3n * 5n)) = 0
(-14 + 6n + (-35n + 15n2)) = 0

Combine like terms: 6n + -35n = -29n
(-14 + -29n + 15n2) = 0

Solving
-14 + -29n + 15n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -5n)(7 + -3n) = 0


Subproblem 1
Set the factor '(-2 + -5n)' equal to zero and attempt to solve:

Simplifying
-2 + -5n = 0

Solving
-2 + -5n = 0

Move all terms containing n to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -5n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5n = 0 + 2
-5n = 0 + 2

Combine like terms: 0 + 2 = 2
-5n = 2

Divide each side by '-5'.
n = -0.4

Simplifying
n = -0.4

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 = {-0.4, 2.333333333}

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