3(x+x+2+x+4)=18+x^2+2x

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Solution for 3(x+x+2+x+4)=18+x^2+2x equation: 


Simplifying
3(x + x + 2 + x + 4) = 18 + x2 + 2x

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

Combine like terms: 2 + 4 = 6
3(6 + x + x + x) = 18 + x2 + 2x

Combine like terms: x + x = 2x
3(6 + 2x + x) = 18 + x2 + 2x

Combine like terms: 2x + x = 3x
3(6 + 3x) = 18 + x2 + 2x
(6 * 3 + 3x * 3) = 18 + x2 + 2x
(18 + 9x) = 18 + x2 + 2x

Reorder the terms:
18 + 9x = 18 + 2x + x2

Add '-18' to each side of the equation.
18 + -18 + 9x = 18 + 2x + -18 + x2

Combine like terms: 18 + -18 = 0
0 + 9x = 18 + 2x + -18 + x2
9x = 18 + 2x + -18 + x2

Reorder the terms:
9x = 18 + -18 + 2x + x2

Combine like terms: 18 + -18 = 0
9x = 0 + 2x + x2
9x = 2x + x2

Solving
9x = 2x + x2

Solving for variable 'x'.

Combine like terms: 9x + -2x = 7x
7x + -1x2 = 2x + x2 + -2x + -1x2

Reorder the terms:
7x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
7x + -1x2 = 0 + x2 + -1x2
7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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