36x+24=12x(x+2+2x)

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Solution for 36x+24=12x(x+2+2x) equation: 


Simplifying
36x + 24 = 12x(x + 2 + 2x)

Reorder the terms:
24 + 36x = 12x(x + 2 + 2x)

Reorder the terms:
24 + 36x = 12x(2 + x + 2x)

Combine like terms: x + 2x = 3x
24 + 36x = 12x(2 + 3x)
24 + 36x = (2 * 12x + 3x * 12x)
24 + 36x = (24x + 36x2)

Solving
24 + 36x = 24x + 36x2

Solving for variable 'x'.

Combine like terms: 36x + -24x = 12x
24 + 12x + -36x2 = 24x + 36x2 + -24x + -36x2

Reorder the terms:
24 + 12x + -36x2 = 24x + -24x + 36x2 + -36x2

Combine like terms: 24x + -24x = 0
24 + 12x + -36x2 = 0 + 36x2 + -36x2
24 + 12x + -36x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
24 + 12x + -36x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(2 + x + -3x2) = 0

Factor a trinomial.
12((1 + -1x)(2 + 3x)) = 0

Ignore the factor 12.

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 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {1, -0.6666666667}

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