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

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


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

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

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

Add '-2' to each side of the equation.
2 + -3x + -2 + -1x2 = 2 + -2 + -2x

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

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

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

Solving
-3x + -1x2 = -2x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(1 + x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, -1}

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