(mx^3+3)(2x^2+5x+2)-(8x^5+20x^4)=m

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Solution for (mx^3+3)(2x^2+5x+2)-(8x^5+20x^4)=m equation: 


Simplifying
(mx3 + 3)(2x2 + 5x + 2) + -1(8x5 + 20x4) = m

Reorder the terms:
(3 + mx3)(2x2 + 5x + 2) + -1(8x5 + 20x4) = m

Reorder the terms:
(3 + mx3)(2 + 5x + 2x2) + -1(8x5 + 20x4) = m

Multiply (3 + mx3) * (2 + 5x + 2x2)
(3(2 + 5x + 2x2) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = m
((2 * 3 + 5x * 3 + 2x2 * 3) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = m
((6 + 15x + 6x2) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = m
(6 + 15x + 6x2 + (2 * mx3 + 5x * mx3 + 2x2 * mx3)) + -1(8x5 + 20x4) = m
(6 + 15x + 6x2 + (2mx3 + 5mx4 + 2mx5)) + -1(8x5 + 20x4) = m

Reorder the terms:
(6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2) + -1(8x5 + 20x4) = m
(6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2) + -1(8x5 + 20x4) = m

Reorder the terms:
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -1(20x4 + 8x5) = m
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + (20x4 * -1 + 8x5 * -1) = m
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + (-20x4 + -8x5) = m

Solving
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = m

Solving for variable 'm'.

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

Add '-1m' to each side of the equation.
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -1m + -8x5 = m + -1m

Reorder the terms:
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = m + -1m

Combine like terms: m + -1m = 0
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0

Add '-6' to each side of the equation.
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -6 + -8x5 = 0 + -6

Reorder the terms:
6 + -6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + -6
-1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + -6

Combine like terms: 0 + -6 = -6
-1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = -6

Add '-15x' to each side of the equation.
-1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -15x + -8x5 = -6 + -15x

Reorder the terms:
-1m + 2mx3 + 5mx4 + 2mx5 + 15x + -15x + 6x2 + -20x4 + -8x5 = -6 + -15x

Combine like terms: 15x + -15x = 0
-1m + 2mx3 + 5mx4 + 2mx5 + 0 + 6x2 + -20x4 + -8x5 = -6 + -15x
-1m + 2mx3 + 5mx4 + 2mx5 + 6x2 + -20x4 + -8x5 = -6 + -15x

Add '-6x2' to each side of the equation.
-1m + 2mx3 + 5mx4 + 2mx5 + 6x2 + -20x4 + -6x2 + -8x5 = -6 + -15x + -6x2

Reorder the terms:
-1m + 2mx3 + 5mx4 + 2mx5 + 6x2 + -6x2 + -20x4 + -8x5 = -6 + -15x + -6x2

Combine like terms: 6x2 + -6x2 = 0
-1m + 2mx3 + 5mx4 + 2mx5 + 0 + -20x4 + -8x5 = -6 + -15x + -6x2
-1m + 2mx3 + 5mx4 + 2mx5 + -20x4 + -8x5 = -6 + -15x + -6x2

Add '20x4' to each side of the equation.
-1m + 2mx3 + 5mx4 + 2mx5 + -20x4 + 20x4 + -8x5 = -6 + -15x + -6x2 + 20x4

Combine like terms: -20x4 + 20x4 = 0
-1m + 2mx3 + 5mx4 + 2mx5 + 0 + -8x5 = -6 + -15x + -6x2 + 20x4
-1m + 2mx3 + 5mx4 + 2mx5 + -8x5 = -6 + -15x + -6x2 + 20x4

Add '8x5' to each side of the equation.
-1m + 2mx3 + 5mx4 + 2mx5 + -8x5 + 8x5 = -6 + -15x + -6x2 + 20x4 + 8x5

Combine like terms: -8x5 + 8x5 = 0
-1m + 2mx3 + 5mx4 + 2mx5 + 0 = -6 + -15x + -6x2 + 20x4 + 8x5
-1m + 2mx3 + 5mx4 + 2mx5 = -6 + -15x + -6x2 + 20x4 + 8x5

Reorder the terms:
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = -6 + -15x + -6x2 + 20x4 + 8x5 + 6 + 15x + 6x2 + -20x4 + -8x5

Reorder the terms:
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = -6 + 6 + -15x + 15x + -6x2 + 6x2 + 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: -6 + 6 = 0
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + -15x + 15x + -6x2 + 6x2 + 20x4 + -20x4 + 8x5 + -8x5
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = -15x + 15x + -6x2 + 6x2 + 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: -15x + 15x = 0
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + -6x2 + 6x2 + 20x4 + -20x4 + 8x5 + -8x5
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = -6x2 + 6x2 + 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: -6x2 + 6x2 = 0
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + 20x4 + -20x4 + 8x5 + -8x5
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: 20x4 + -20x4 = 0
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0 + 8x5 + -8x5
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 8x5 + -8x5

Combine like terms: 8x5 + -8x5 = 0
6 + -1m + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 0

The solution to this equation could not be determined.

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