(5x-1)x+(x-1)(x+1)=0

Solution for (5x-1)x+(x-1)(x+1)=0 equation:

Simplifying
(5x + -1) * x + (x + -1)(x + 1) = 0

Reorder the terms:
(-1 + 5x) * x + (x + -1)(x + 1) = 0

Reorder the terms for easier multiplication:
x(-1 + 5x) + (x + -1)(x + 1) = 0
(-1 * x + 5x * x) + (x + -1)(x + 1) = 0
(-1x + 5x2) + (x + -1)(x + 1) = 0

Reorder the terms:
-1x + 5x2 + (-1 + x)(x + 1) = 0

Reorder the terms:
-1x + 5x2 + (-1 + x)(1 + x) = 0

Multiply (-1 + x) * (1 + x)
-1x + 5x2 + (-1(1 + x) + x(1 + x)) = 0
-1x + 5x2 + ((1 * -1 + x * -1) + x(1 + x)) = 0
-1x + 5x2 + ((-1 + -1x) + x(1 + x)) = 0
-1x + 5x2 + (-1 + -1x + (1 * x + x * x)) = 0
-1x + 5x2 + (-1 + -1x + (1x + x2)) = 0

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

Reorder the terms:
-1 + -1x + 5x2 + x2 = 0

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

Solving
-1 + -1x + 6x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-0.3333333333, 0.5}