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

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


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

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

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

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

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

Reorder the terms:
-14 + 5x + x2 = 2(2 + x)
-14 + 5x + x2 = (2 * 2 + x * 2)
-14 + 5x + x2 = (4 + 2x)

Solving
-14 + 5x + x2 = 4 + 2x

Solving for variable 'x'.

Reorder the terms:
-14 + -4 + 5x + -2x + x2 = 4 + 2x + -4 + -2x

Combine like terms: -14 + -4 = -18
-18 + 5x + -2x + x2 = 4 + 2x + -4 + -2x

Combine like terms: 5x + -2x = 3x
-18 + 3x + x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-18 + 3x + x2 = 4 + -4 + 2x + -2x

Combine like terms: 4 + -4 = 0
-18 + 3x + x2 = 0 + 2x + -2x
-18 + 3x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-18 + 3x + x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-6, 3}

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