-3x^2+16x-13=0

Solution for -3x^2+16x-13=0 equation:

Simplifying
-3x2 + 16x + -13 = 0

Reorder the terms:
-13 + 16x + -3x2 = 0

Solving
-13 + 16x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + 3x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-13 + 3x)' equal to zero and attempt to solve:

Simplifying
-13 + 3x = 0

Solving
-13 + 3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 3x = 0 + 13
3x = 0 + 13

Combine like terms: 0 + 13 = 13
3x = 13

Divide each side by '3'.
x = 4.333333333

Simplifying
x = 4.333333333
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {4.333333333, 1}