x(x+2)=5(x+4)-2

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Solution for x(x+2)=5(x+4)-2 equation: 


Simplifying
x(x + 2) = 5(x + 4) + -2

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

Reorder the terms:
2x + x2 = 5(4 + x) + -2
2x + x2 = (4 * 5 + x * 5) + -2
2x + x2 = (20 + 5x) + -2

Reorder the terms:
2x + x2 = 20 + -2 + 5x

Combine like terms: 20 + -2 = 18
2x + x2 = 18 + 5x

Solving
2x + x2 = 18 + 5x

Solving for variable 'x'.

Reorder the terms:
-18 + 2x + -5x + x2 = 18 + 5x + -18 + -5x

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

Reorder the terms:
-18 + -3x + x2 = 18 + -18 + 5x + -5x

Combine like terms: 18 + -18 = 0
-18 + -3x + x2 = 0 + 5x + -5x
-18 + -3x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-3, 6}

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