(6x^2)-13x=8

Solution for (6x^2)-13x=8 equation:

Simplifying
(6x2) + -13x = 8

Reorder the terms:
-13x + (6x2) = 8

Solving
-13x + (6x2) = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -13x + (6x2) = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -13x + (6x2) = 0

Factor a trinomial.
(-1 + -2x)(8 + -3x) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

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

Simplifying
x = -0.5
Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-0.5, 2.666666667}