-10n^2+13n-18=(-9n+3)(n-2)

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Solution for -10n^2+13n-18=(-9n+3)(n-2) equation: 


Simplifying
-10n2 + 13n + -18 = (-9n + 3)(n + -2)

Reorder the terms:
-18 + 13n + -10n2 = (-9n + 3)(n + -2)

Reorder the terms:
-18 + 13n + -10n2 = (3 + -9n)(n + -2)

Reorder the terms:
-18 + 13n + -10n2 = (3 + -9n)(-2 + n)

Multiply (3 + -9n) * (-2 + n)
-18 + 13n + -10n2 = (3(-2 + n) + -9n * (-2 + n))
-18 + 13n + -10n2 = ((-2 * 3 + n * 3) + -9n * (-2 + n))
-18 + 13n + -10n2 = ((-6 + 3n) + -9n * (-2 + n))
-18 + 13n + -10n2 = (-6 + 3n + (-2 * -9n + n * -9n))
-18 + 13n + -10n2 = (-6 + 3n + (18n + -9n2))

Combine like terms: 3n + 18n = 21n
-18 + 13n + -10n2 = (-6 + 21n + -9n2)

Solving
-18 + 13n + -10n2 = -6 + 21n + -9n2

Solving for variable 'n'.

Reorder the terms:
-18 + 6 + 13n + -21n + -10n2 + 9n2 = -6 + 21n + -9n2 + 6 + -21n + 9n2

Combine like terms: -18 + 6 = -12
-12 + 13n + -21n + -10n2 + 9n2 = -6 + 21n + -9n2 + 6 + -21n + 9n2

Combine like terms: 13n + -21n = -8n
-12 + -8n + -10n2 + 9n2 = -6 + 21n + -9n2 + 6 + -21n + 9n2

Combine like terms: -10n2 + 9n2 = -1n2
-12 + -8n + -1n2 = -6 + 21n + -9n2 + 6 + -21n + 9n2

Reorder the terms:
-12 + -8n + -1n2 = -6 + 6 + 21n + -21n + -9n2 + 9n2

Combine like terms: -6 + 6 = 0
-12 + -8n + -1n2 = 0 + 21n + -21n + -9n2 + 9n2
-12 + -8n + -1n2 = 21n + -21n + -9n2 + 9n2

Combine like terms: 21n + -21n = 0
-12 + -8n + -1n2 = 0 + -9n2 + 9n2
-12 + -8n + -1n2 = -9n2 + 9n2

Combine like terms: -9n2 + 9n2 = 0
-12 + -8n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 8n + n2) = 0

Factor a trinomial.
-1((6 + n)(2 + n)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6

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

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {-6, -2}

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