4x^2-1-x(2x+1)=0

Solution for 4x^2-1-x(2x+1)=0 equation:

Simplifying
4x2 + -1 + -1x(2x + 1) = 0

Reorder the terms:
4x2 + -1 + -1x(1 + 2x) = 0
4x2 + -1 + (1 * -1x + 2x * -1x) = 0
4x2 + -1 + (-1x + -2x2) = 0

Reorder the terms:
-1 + -1x + 4x2 + -2x2 = 0

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

Solving
-1 + -1x + 2x2 = 0

Solving for variable 'x'.

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