(x(x+2))+(5(x-2))=8

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Solution for (x(x+2))+(5(x-2))=8 equation: 


Simplifying
(x(x + 2)) + (5(x + -2)) = 8

Reorder the terms:
(x(2 + x)) + (5(x + -2)) = 8
((2 * x + x * x)) + (5(x + -2)) = 8
((2x + x2)) + (5(x + -2)) = 8
(2x + x2) + (5(x + -2)) = 8

Remove parenthesis around (2x + x2)
2x + x2 + (5(x + -2)) = 8

Reorder the terms:
2x + x2 + (5(-2 + x)) = 8
2x + x2 + ((-2 * 5 + x * 5)) = 8
2x + x2 + ((-10 + 5x)) = 8
2x + x2 + (-10 + 5x) = 8

Remove parenthesis around (-10 + 5x)
2x + x2 + -10 + 5x = 8

Reorder the terms:
-10 + 2x + 5x + x2 = 8

Combine like terms: 2x + 5x = 7x
-10 + 7x + x2 = 8

Solving
-10 + 7x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-10 + -8 + 7x + x2 = 8 + -8

Combine like terms: -10 + -8 = -18
-18 + 7x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-18 + 7x + x2 = 0

Factor a trinomial.
(-9 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

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

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

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
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
Solution
x = {-9, 2}

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