3x(1+x)+6(x^2-4x)=

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Solution for 3x(1+x)+6(x^2-4x)= equation: 


Simplifying
3x(1 + x) + 6(x2 + -4x) = 0
(1 * 3x + x * 3x) + 6(x2 + -4x) = 0
(3x + 3x2) + 6(x2 + -4x) = 0

Reorder the terms:
3x + 3x2 + 6(-4x + x2) = 0
3x + 3x2 + (-4x * 6 + x2 * 6) = 0
3x + 3x2 + (-24x + 6x2) = 0

Reorder the terms:
3x + -24x + 3x2 + 6x2 = 0

Combine like terms: 3x + -24x = -21x
-21x + 3x2 + 6x2 = 0

Combine like terms: 3x2 + 6x2 = 9x2
-21x + 9x2 = 0

Solving
-21x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-7 + 3x) = 0

Ignore the factor 3.

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

Simplifying
-7 + 3x = 0

Solving
-7 + 3x = 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 + 3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x = 0 + 7
3x = 0 + 7

Combine like terms: 0 + 7 = 7
3x = 7

Divide each side by '3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0, 2.333333333}

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