5x^2=13x-6

Solution for 5x^2=13x-6 equation:

Simplifying
5x2 = 13x + -6

Reorder the terms:
5x2 = -6 + 13x

Solving
5x2 = -6 + 13x

Solving for variable 'x'.

Reorder the terms:
6 + -13x + 5x2 = -6 + 13x + 6 + -13x

Reorder the terms:
6 + -13x + 5x2 = -6 + 6 + 13x + -13x

Combine like terms: -6 + 6 = 0
6 + -13x + 5x2 = 0 + 13x + -13x
6 + -13x + 5x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
6 + -13x + 5x2 = 0

Factor a trinomial.
(3 + -5x)(2 + -1x) = 0

Subproblem 1
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.6, 2}