5x^2-21x+13=-5

Solution for 5x^2-21x+13=-5 equation:

Simplifying
5x2 + -21x + 13 = -5

Reorder the terms:
13 + -21x + 5x2 = -5

Solving
13 + -21x + 5x2 = -5

Solving for variable 'x'.

Reorder the terms:
13 + 5 + -21x + 5x2 = -5 + 5

Combine like terms: 13 + 5 = 18
18 + -21x + 5x2 = -5 + 5

Combine like terms: -5 + 5 = 0
18 + -21x + 5x2 = 0

Factor a trinomial.
(6 + -5x)(3 + -1x) = 0

Subproblem 1
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.2, 3}