10n^2-13n=-4

Solution for 10n^2-13n=-4 equation:

Simplifying
10n2 + -13n = -4

Reorder the terms:
-13n + 10n2 = -4

Solving
-13n + 10n2 = -4

Solving for variable 'n'.

Reorder the terms:
4 + -13n + 10n2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + -13n + 10n2 = 0

Factor a trinomial.
(1 + -2n)(4 + -5n) = 0

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Solution
n = {0.5, 0.8}