4(x+3)+2x=6x(x+2)

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Solution for 4(x+3)+2x=6x(x+2) equation: 


Simplifying
4(x + 3) + 2x = 6x(x + 2)

Reorder the terms:
4(3 + x) + 2x = 6x(x + 2)
(3 * 4 + x * 4) + 2x = 6x(x + 2)
(12 + 4x) + 2x = 6x(x + 2)

Combine like terms: 4x + 2x = 6x
12 + 6x = 6x(x + 2)

Reorder the terms:
12 + 6x = 6x(2 + x)
12 + 6x = (2 * 6x + x * 6x)
12 + 6x = (12x + 6x2)

Solving
12 + 6x = 12x + 6x2

Solving for variable 'x'.

Combine like terms: 6x + -12x = -6x
12 + -6x + -6x2 = 12x + 6x2 + -12x + -6x2

Reorder the terms:
12 + -6x + -6x2 = 12x + -12x + 6x2 + -6x2

Combine like terms: 12x + -12x = 0
12 + -6x + -6x2 = 0 + 6x2 + -6x2
12 + -6x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
12 + -6x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -1x + -1x2) = 0

Factor a trinomial.
6((1 + -1x)(2 + x)) = 0

Ignore the factor 6.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {1, -2}

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