-x(4x-3)=-1

Solution for -x(4x-3)=-1 equation:

Simplifying
-1x(4x + -3) = -1

Reorder the terms:
-1x(-3 + 4x) = -1
(-3 * -1x + 4x * -1x) = -1
(3x + -4x2) = -1

Solving
3x + -4x2 = -1

Solving for variable 'x'.

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

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

Factor a trinomial.
(1 + -1x)(1 + 4x) = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

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

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

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {1, -0.25}