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

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


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

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

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

Reorder the terms:
6x + 3x2 = -5 + -1x + x2

Solving
6x + 3x2 = -5 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
5 + 6x + x + 3x2 + -1x2 = -5 + -1x + x2 + 5 + x + -1x2

Combine like terms: 6x + x = 7x
5 + 7x + 3x2 + -1x2 = -5 + -1x + x2 + 5 + x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
5 + 7x + 2x2 = -5 + -1x + x2 + 5 + x + -1x2

Reorder the terms:
5 + 7x + 2x2 = -5 + 5 + -1x + x + x2 + -1x2

Combine like terms: -5 + 5 = 0
5 + 7x + 2x2 = 0 + -1x + x + x2 + -1x2
5 + 7x + 2x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
5 + 7x + 2x2 = 0 + x2 + -1x2
5 + 7x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + 7x + 2x2 = 0

Factor a trinomial.
(5 + 2x)(1 + x) = 0


Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, -1}

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