2-x=(x-2)(x+7)

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Solution for 2-x=(x-2)(x+7) equation: 


Simplifying
2 + -1x = (x + -2)(x + 7)

Reorder the terms:
2 + -1x = (-2 + x)(x + 7)

Reorder the terms:
2 + -1x = (-2 + x)(7 + x)

Multiply (-2 + x) * (7 + x)
2 + -1x = (-2(7 + x) + x(7 + x))
2 + -1x = ((7 * -2 + x * -2) + x(7 + x))
2 + -1x = ((-14 + -2x) + x(7 + x))
2 + -1x = (-14 + -2x + (7 * x + x * x))
2 + -1x = (-14 + -2x + (7x + x2))

Combine like terms: -2x + 7x = 5x
2 + -1x = (-14 + 5x + x2)

Solving
2 + -1x = -14 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
2 + 14 + -1x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: 2 + 14 = 16
16 + -1x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: -1x + -5x = -6x
16 + -6x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Reorder the terms:
16 + -6x + -1x2 = -14 + 14 + 5x + -5x + x2 + -1x2

Combine like terms: -14 + 14 = 0
16 + -6x + -1x2 = 0 + 5x + -5x + x2 + -1x2
16 + -6x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
16 + -6x + -1x2 = 0 + x2 + -1x2
16 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -6x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(8 + x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {2, -8}

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