3x(x+2)-2=-(5+x)+x

Solution for 3x(x+2)-2=-(5+x)+x equation:

Simplifying
3x(x + 2) + -2 = -1(5 + x) + x

Reorder the terms:
3x(2 + x) + -2 = -1(5 + x) + x
(2 * 3x + x * 3x) + -2 = -1(5 + x) + x
(6x + 3x2) + -2 = -1(5 + x) + x

Reorder the terms:
-2 + 6x + 3x2 = -1(5 + x) + x
-2 + 6x + 3x2 = (5 * -1 + x * -1) + x
-2 + 6x + 3x2 = (-5 + -1x) + x

Combine like terms: -1x + x = 0
-2 + 6x + 3x2 = -5 + 0
-2 + 6x + 3x2 = -5

Solving
-2 + 6x + 3x2 = -5

Solving for variable 'x'.

Reorder the terms:
-2 + 5 + 6x + 3x2 = -5 + 5

Combine like terms: -2 + 5 = 3
3 + 6x + 3x2 = -5 + 5

Combine like terms: -5 + 5 = 0
3 + 6x + 3x2 = 0

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

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

Ignore the factor 3.
Subproblem 1
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
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 = {-1, -1}