3x=x(2x+4)

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


Simplifying
3x = x(2x + 4)

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

Solving
3x = 4x + 2x2

Solving for variable 'x'.

Combine like terms: 3x + -4x = -1x
-1x + -2x2 = 4x + 2x2 + -4x + -2x2

Reorder the terms:
-1x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
-1x + -2x2 = 0 + 2x2 + -2x2
-1x + -2x2 = 2x2 + -2x2

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

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

Ignore the factor -1.

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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -0.5}

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