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

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

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

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

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

Solving
1 + 3x + -1x2 = -1 + 4x

Solving for variable 'x'.

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

Combine like terms: 1 + 1 = 2
2 + 3x + -4x + -1x2 = -1 + 4x + 1 + -4x

Combine like terms: 3x + -4x = -1x
2 + -1x + -1x2 = -1 + 4x + 1 + -4x

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

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

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

Factor a trinomial.
(1 + -1x)(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {1, -2}