3x-1=4-x^2-x

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Solution for 3x-1=4-x^2-x equation: 


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -1 + -4 = -5
-5 + 3x + x + x2 = 4 + -1x + -1x2 + -4 + x + x2

Combine like terms: 3x + x = 4x
-5 + 4x + x2 = 4 + -1x + -1x2 + -4 + x + x2

Reorder the terms:
-5 + 4x + x2 = 4 + -4 + -1x + x + -1x2 + x2

Combine like terms: 4 + -4 = 0
-5 + 4x + x2 = 0 + -1x + x + -1x2 + x2
-5 + 4x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-5 + 4x + x2 = 0 + -1x2 + x2
-5 + 4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-5 + 4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -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 = {-5, 1}

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