6x^2+13x-5=(3x-1)

Solution for 6x^2+13x-5=(3x-1) equation:

Simplifying
6x2 + 13x + -5 = (3x + -1)

Reorder the terms:
-5 + 13x + 6x2 = (3x + -1)

Reorder the terms:
-5 + 13x + 6x2 = (-1 + 3x)

Remove parenthesis around (-1 + 3x)
-5 + 13x + 6x2 = -1 + 3x

Solving
-5 + 13x + 6x2 = -1 + 3x

Solving for variable 'x'.

Reorder the terms:
-5 + 1 + 13x + -3x + 6x2 = -1 + 3x + 1 + -3x

Combine like terms: -5 + 1 = -4
-4 + 13x + -3x + 6x2 = -1 + 3x + 1 + -3x

Combine like terms: 13x + -3x = 10x
-4 + 10x + 6x2 = -1 + 3x + 1 + -3x

Reorder the terms:
-4 + 10x + 6x2 = -1 + 1 + 3x + -3x

Combine like terms: -1 + 1 = 0
-4 + 10x + 6x2 = 0 + 3x + -3x
-4 + 10x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + 10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5x + 3x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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, 0.3333333333}