2-x(x-1)=4-(x+3)2

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


Simplifying
2 + -1x(x + -1) = 4 + -1(x + 3) * 2

Reorder the terms:
2 + -1x(-1 + x) = 4 + -1(x + 3) * 2
2 + (-1 * -1x + x * -1x) = 4 + -1(x + 3) * 2
2 + (1x + -1x2) = 4 + -1(x + 3) * 2

Reorder the terms:
2 + 1x + -1x2 = 4 + -1(3 + x) * 2

Reorder the terms for easier multiplication:
2 + 1x + -1x2 = 4 + -1 * 2(3 + x)

Multiply -1 * 2
2 + 1x + -1x2 = 4 + -2(3 + x)
2 + 1x + -1x2 = 4 + (3 * -2 + x * -2)
2 + 1x + -1x2 = 4 + (-6 + -2x)

Combine like terms: 4 + -6 = -2
2 + 1x + -1x2 = -2 + -2x

Solving
2 + 1x + -1x2 = -2 + -2x

Solving for variable 'x'.

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

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

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

Reorder the terms:
4 + 3x + -1x2 = -2 + 2 + -2x + 2x

Combine like terms: -2 + 2 = 0
4 + 3x + -1x2 = 0 + -2x + 2x
4 + 3x + -1x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
4 + 3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(1 + x) = 0


Subproblem 1
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

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

Simplifying
1 + x = 0

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

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

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

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

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