3x(2x-1)+8x=1

Solution for 3x(2x-1)+8x=1 equation:

Simplifying
3x(2x + -1) + 8x = 1

Reorder the terms:
3x(-1 + 2x) + 8x = 1
(-1 * 3x + 2x * 3x) + 8x = 1
(-3x + 6x2) + 8x = 1

Reorder the terms:
-3x + 8x + 6x2 = 1

Combine like terms: -3x + 8x = 5x
5x + 6x2 = 1

Solving
5x + 6x2 = 1

Solving for variable 'x'.

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

Combine like terms: 1 + -1 = 0
-1 + 5x + 6x2 = 0

Factor a trinomial.
(-1 + -1x)(1 + -6x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {-1, 0.1666666667}