8-3x(x+2)=2-3x

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Solution for 8-3x(x+2)=2-3x equation: 


Simplifying
8 + -3x(x + 2) = 2 + -3x

Reorder the terms:
8 + -3x(2 + x) = 2 + -3x
8 + (2 * -3x + x * -3x) = 2 + -3x
8 + (-6x + -3x2) = 2 + -3x

Solving
8 + -6x + -3x2 = 2 + -3x

Solving for variable 'x'.

Reorder the terms:
8 + -2 + -6x + 3x + -3x2 = 2 + -3x + -2 + 3x

Combine like terms: 8 + -2 = 6
6 + -6x + 3x + -3x2 = 2 + -3x + -2 + 3x

Combine like terms: -6x + 3x = -3x
6 + -3x + -3x2 = 2 + -3x + -2 + 3x

Reorder the terms:
6 + -3x + -3x2 = 2 + -2 + -3x + 3x

Combine like terms: 2 + -2 = 0
6 + -3x + -3x2 = 0 + -3x + 3x
6 + -3x + -3x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
6 + -3x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1x + -1x2) = 0

Factor a trinomial.
3((1 + -1x)(2 + x)) = 0

Ignore the factor 3.

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {1, -2}

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