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

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Solution for 10(x+2)=(x-1)(x+2) equation: 


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

Reorder the terms:
10(2 + x) = (x + -1)(x + 2)
(2 * 10 + x * 10) = (x + -1)(x + 2)
(20 + 10x) = (x + -1)(x + 2)

Reorder the terms:
20 + 10x = (-1 + x)(x + 2)

Reorder the terms:
20 + 10x = (-1 + x)(2 + x)

Multiply (-1 + x) * (2 + x)
20 + 10x = (-1(2 + x) + x(2 + x))
20 + 10x = ((2 * -1 + x * -1) + x(2 + x))
20 + 10x = ((-2 + -1x) + x(2 + x))
20 + 10x = (-2 + -1x + (2 * x + x * x))
20 + 10x = (-2 + -1x + (2x + x2))

Combine like terms: -1x + 2x = 1x
20 + 10x = (-2 + 1x + x2)

Solving
20 + 10x = -2 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
20 + 2 + 10x + -1x + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 20 + 2 = 22
22 + 10x + -1x + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 10x + -1x = 9x
22 + 9x + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Reorder the terms:
22 + 9x + -1x2 = -2 + 2 + 1x + -1x + x2 + -1x2

Combine like terms: -2 + 2 = 0
22 + 9x + -1x2 = 0 + 1x + -1x + x2 + -1x2
22 + 9x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
22 + 9x + -1x2 = 0 + x2 + -1x2
22 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
22 + 9x + -1x2 = 0

Factor a trinomial.
(11 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11

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 = {11, -2}

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