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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
-2 + 1x + x2 = 1 + -1 + 3x + -3x + -1x2 + x2

Combine like terms: 1 + -1 = 0
-2 + 1x + x2 = 0 + 3x + -3x + -1x2 + x2
-2 + 1x + x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
-2 + 1x + x2 = 0 + -1x2 + x2
-2 + 1x + x2 = -1x2 + x2

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

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


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1}

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