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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
4 + -5x + x2 = -3 + 3 + 4x + -4x + -1x2 + x2

Combine like terms: -3 + 3 = 0
4 + -5x + x2 = 0 + 4x + -4x + -1x2 + x2
4 + -5x + x2 = 4x + -4x + -1x2 + x2

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

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

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}

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