3x-x-5=2x(x+2)-9

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Solution for 3x-x-5=2x(x+2)-9 equation: 


Simplifying
3x + -1x + -5 = 2x(x + 2) + -9

Reorder the terms:
-5 + 3x + -1x = 2x(x + 2) + -9

Combine like terms: 3x + -1x = 2x
-5 + 2x = 2x(x + 2) + -9

Reorder the terms:
-5 + 2x = 2x(2 + x) + -9
-5 + 2x = (2 * 2x + x * 2x) + -9
-5 + 2x = (4x + 2x2) + -9

Reorder the terms:
-5 + 2x = -9 + 4x + 2x2

Solving
-5 + 2x = -9 + 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 9 + 2x + -4x + -2x2 = -9 + 4x + 2x2 + 9 + -4x + -2x2

Combine like terms: -5 + 9 = 4
4 + 2x + -4x + -2x2 = -9 + 4x + 2x2 + 9 + -4x + -2x2

Combine like terms: 2x + -4x = -2x
4 + -2x + -2x2 = -9 + 4x + 2x2 + 9 + -4x + -2x2

Reorder the terms:
4 + -2x + -2x2 = -9 + 9 + 4x + -4x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
4 + -2x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
4 + -2x + -2x2 = 4x + -4x + 2x2 + -2x2

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

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

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

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

Ignore the factor 2.

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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