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

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


Simplifying
(3x)(x + x) = 2x2 + 6x

Remove parenthesis around (3x)
3x(x + x) = 2x2 + 6x

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

Remove parenthesis around (2x)
3x * 2x = 2x2 + 6x

Reorder the terms for easier multiplication:
3 * 2x * x = 2x2 + 6x

Multiply 3 * 2
6x * x = 2x2 + 6x

Multiply x * x
6x2 = 2x2 + 6x

Reorder the terms:
6x2 = 6x + 2x2

Solving
6x2 = 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-6x + 6x2 + -2x2 = 6x + 2x2 + -6x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-6x + 4x2 = 6x + 2x2 + -6x + -2x2

Reorder the terms:
-6x + 4x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
-6x + 4x2 = 0 + 2x2 + -2x2
-6x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6x + 4x2 = 0

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

Ignore the factor 2.

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 '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

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

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

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

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 1.5}

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