(6+3x)(x+14)x=

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Solution for (6+3x)(x+14)x= equation: 


Simplifying
(6 + 3x)(x + 14) * x = 0

Reorder the terms:
(6 + 3x)(14 + x) * x = 0

Reorder the terms for easier multiplication:
x(6 + 3x)(14 + x) = 0

Multiply (6 + 3x) * (14 + x)
x(6(14 + x) + 3x * (14 + x)) = 0
x((14 * 6 + x * 6) + 3x * (14 + x)) = 0
x((84 + 6x) + 3x * (14 + x)) = 0
x(84 + 6x + (14 * 3x + x * 3x)) = 0
x(84 + 6x + (42x + 3x2)) = 0

Combine like terms: 6x + 42x = 48x
x(84 + 48x + 3x2) = 0
(84 * x + 48x * x + 3x2 * x) = 0
(84x + 48x2 + 3x3) = 0

Solving
84x + 48x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(28 + 16x + x2) = 0

Factor a trinomial.
3x((14 + x)(2 + x)) = 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 '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14

Subproblem 3
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 = {0, -14, -2}

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