6*x^2+13*x=5

Solution for 6*x^2+13*x=5 equation:

Simplifying
6x2 + 13x = 5

Reorder the terms:
13x + 6x2 = 5

Solving
13x + 6x2 = 5

Solving for variable 'x'.

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

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

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

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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-2.5, 0.3333333333}