5n^2+46n-10=7n-2

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Solution for 5n^2+46n-10=7n-2 equation: 


Simplifying
5n2 + 46n + -10 = 7n + -2

Reorder the terms:
-10 + 46n + 5n2 = 7n + -2

Reorder the terms:
-10 + 46n + 5n2 = -2 + 7n

Solving
-10 + 46n + 5n2 = -2 + 7n

Solving for variable 'n'.

Reorder the terms:
-10 + 2 + 46n + -7n + 5n2 = -2 + 7n + 2 + -7n

Combine like terms: -10 + 2 = -8
-8 + 46n + -7n + 5n2 = -2 + 7n + 2 + -7n

Combine like terms: 46n + -7n = 39n
-8 + 39n + 5n2 = -2 + 7n + 2 + -7n

Reorder the terms:
-8 + 39n + 5n2 = -2 + 2 + 7n + -7n

Combine like terms: -2 + 2 = 0
-8 + 39n + 5n2 = 0 + 7n + -7n
-8 + 39n + 5n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-8 + 39n + 5n2 = 0

Factor a trinomial.
(-8 + -1n)(1 + -5n) = 0


Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8

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

Simplifying
1 + -5n = 0

Solving
1 + -5n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5n = 0 + -1
-5n = 0 + -1

Combine like terms: 0 + -1 = -1
-5n = -1

Divide each side by '-5'.
n = 0.2

Simplifying
n = 0.2
Solution
n = {-8, 0.2}

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