x(4x-1)=x+2

Solution for x(4x-1)=x+2 equation:

Simplifying
x(4x + -1) = x + 2

Reorder the terms:
x(-1 + 4x) = x + 2
(-1 * x + 4x * x) = x + 2
(-1x + 4x2) = x + 2

Reorder the terms:
-1x + 4x2 = 2 + x

Solving
-1x + 4x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
-2 + -1x + -1x + 4x2 = 2 + x + -2 + -1x

Combine like terms: -1x + -1x = -2x
-2 + -2x + 4x2 = 2 + x + -2 + -1x

Reorder the terms:
-2 + -2x + 4x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
-2 + -2x + 4x2 = 0 + x + -1x
-2 + -2x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
-2 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1x + 2x2) = 0

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

Ignore the factor 2.
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 '(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
Solution
x = {-0.5, 1}