P(x)=3x(2+4x)+(sx+2)2x

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


Simplifying
P(x) = 3x(2 + 4x) + (sx + 2) * 2x

Multiply P * x
xP = 3x(2 + 4x) + (sx + 2) * 2x
xP = (2 * 3x + 4x * 3x) + (sx + 2) * 2x
xP = (6x + 12x2) + (sx + 2) * 2x

Reorder the terms:
xP = 6x + 12x2 + (2 + sx) * 2x

Reorder the terms for easier multiplication:
xP = 6x + 12x2 + 2x(2 + sx)
xP = 6x + 12x2 + (2 * 2x + sx * 2x)

Reorder the terms:
xP = 6x + 12x2 + (2sx2 + 4x)
xP = 6x + 12x2 + (2sx2 + 4x)

Reorder the terms:
xP = 2sx2 + 6x + 4x + 12x2

Combine like terms: 6x + 4x = 10x
xP = 2sx2 + 10x + 12x2

Solving
xP = 2sx2 + 10x + 12x2

Solving for variable 'x'.

Reorder the terms:
-2sx2 + -10x + xP + -12x2 = 2sx2 + 10x + 12x2 + -2sx2 + -10x + -12x2

Reorder the terms:
-2sx2 + -10x + xP + -12x2 = 2sx2 + -2sx2 + 10x + -10x + 12x2 + -12x2

Combine like terms: 2sx2 + -2sx2 = 0
-2sx2 + -10x + xP + -12x2 = 0 + 10x + -10x + 12x2 + -12x2
-2sx2 + -10x + xP + -12x2 = 10x + -10x + 12x2 + -12x2

Combine like terms: 10x + -10x = 0
-2sx2 + -10x + xP + -12x2 = 0 + 12x2 + -12x2
-2sx2 + -10x + xP + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-2sx2 + -10x + xP + -12x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2sx + -10 + P + -12x) = 0


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 '(-2sx + -10 + P + -12x)' equal to zero and attempt to solve:

Simplifying
-2sx + -10 + P + -12x = 0

Reorder the terms:
-10 + P + -2sx + -12x = 0

Solving
-10 + P + -2sx + -12x = 0

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

Add '10' to each side of the equation.
-10 + P + -2sx + 10 + -12x = 0 + 10

Reorder the terms:
-10 + 10 + P + -2sx + -12x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + P + -2sx + -12x = 0 + 10
P + -2sx + -12x = 0 + 10

Combine like terms: 0 + 10 = 10
P + -2sx + -12x = 10

Add '-1P' to each side of the equation.
P + -2sx + -1P + -12x = 10 + -1P

Reorder the terms:
P + -1P + -2sx + -12x = 10 + -1P

Combine like terms: P + -1P = 0
0 + -2sx + -12x = 10 + -1P
-2sx + -12x = 10 + -1P

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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