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

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

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

Reorder the terms:
5(2 + x) = (x + -1)(x + 2)
(2 * 5 + x * 5) = (x + -1)(x + 2)
(10 + 5x) = (x + -1)(x + 2)

Reorder the terms:
10 + 5x = (-1 + x)(x + 2)

Reorder the terms:
10 + 5x = (-1 + x)(2 + x)

Multiply (-1 + x) * (2 + x)
10 + 5x = (-1(2 + x) + x(2 + x))
10 + 5x = ((2 * -1 + x * -1) + x(2 + x))
10 + 5x = ((-2 + -1x) + x(2 + x))
10 + 5x = (-2 + -1x + (2 * x + x * x))
10 + 5x = (-2 + -1x + (2x + x2))

Combine like terms: -1x + 2x = 1x
10 + 5x = (-2 + 1x + x2)

Solving
10 + 5x = -2 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
10 + 2 + 5x + -1x + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 10 + 2 = 12
12 + 5x + -1x + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 5x + -1x = 4x
12 + 4x + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Reorder the terms:
12 + 4x + -1x2 = -2 + 2 + 1x + -1x + x2 + -1x2

Combine like terms: -2 + 2 = 0
12 + 4x + -1x2 = 0 + 1x + -1x + x2 + -1x2
12 + 4x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
12 + 4x + -1x2 = 0 + x2 + -1x2
12 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 4x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
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 = {6, -2}