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

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Solution for 3x-1=2x(x+2)-5+x equation:


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

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

Reorder the terms:
-1 + 3x = 2x(2 + x) + -5 + x
-1 + 3x = (2 * 2x + x * 2x) + -5 + x
-1 + 3x = (4x + 2x2) + -5 + x

Reorder the terms:
-1 + 3x = -5 + 4x + x + 2x2

Combine like terms: 4x + x = 5x
-1 + 3x = -5 + 5x + 2x2

Solving
-1 + 3x = -5 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-1 + 5 + 3x + -5x + -2x2 = -5 + 5x + 2x2 + 5 + -5x + -2x2

Combine like terms: -1 + 5 = 4
4 + 3x + -5x + -2x2 = -5 + 5x + 2x2 + 5 + -5x + -2x2

Combine like terms: 3x + -5x = -2x
4 + -2x + -2x2 = -5 + 5x + 2x2 + 5 + -5x + -2x2

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

Combine like terms: -5 + 5 = 0
4 + -2x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
4 + -2x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 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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