(mx^3+3)(2x^2+5x+2)-(8x^5+20x^4)=8x^3+6x^2+15+6

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Solution for (mx^3+3)(2x^2+5x+2)-(8x^5+20x^4)=8x^3+6x^2+15+6 equation: 


Simplifying
(mx3 + 3)(2x2 + 5x + 2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6

Reorder the terms:
(3 + mx3)(2x2 + 5x + 2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6

Reorder the terms:
(3 + mx3)(2 + 5x + 2x2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6

Multiply (3 + mx3) * (2 + 5x + 2x2)
(3(2 + 5x + 2x2) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6
((2 * 3 + 5x * 3 + 2x2 * 3) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6
((6 + 15x + 6x2) + mx3(2 + 5x + 2x2)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6
(6 + 15x + 6x2 + (2 * mx3 + 5x * mx3 + 2x2 * mx3)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6
(6 + 15x + 6x2 + (2mx3 + 5mx4 + 2mx5)) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6

Reorder the terms:
(6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6
(6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2) + -1(8x5 + 20x4) = 8x3 + 6x2 + 15 + 6

Reorder the terms:
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -1(20x4 + 8x5) = 8x3 + 6x2 + 15 + 6
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + (20x4 * -1 + 8x5 * -1) = 8x3 + 6x2 + 15 + 6
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + (-20x4 + -8x5) = 8x3 + 6x2 + 15 + 6

Reorder the terms:
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 15 + 6 + 6x2 + 8x3

Combine like terms: 15 + 6 = 21
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -8x5 = 21 + 6x2 + 8x3

Add '-6x2' to each side of the equation.
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -20x4 + -6x2 + -8x5 = 21 + 6x2 + -6x2 + 8x3

Reorder the terms:
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 6x2 + -6x2 + -20x4 + -8x5 = 21 + 6x2 + -6x2 + 8x3

Combine like terms: 6x2 + -6x2 = 0
6 + 2mx3 + 5mx4 + 2mx5 + 15x + 0 + -20x4 + -8x5 = 21 + 6x2 + -6x2 + 8x3
6 + 2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 21 + 6x2 + -6x2 + 8x3

Combine like terms: 6x2 + -6x2 = 0
6 + 2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 21 + 0 + 8x3
6 + 2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 21 + 8x3

Solving
6 + 2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 21 + 8x3

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + 2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -6 + -8x5 = 21 + -6 + 8x3

Reorder the terms:
6 + -6 + 2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 21 + -6 + 8x3

Combine like terms: 6 + -6 = 0
0 + 2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 21 + -6 + 8x3
2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 21 + -6 + 8x3

Combine like terms: 21 + -6 = 15
2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -8x5 = 15 + 8x3

Add '-15x' to each side of the equation.
2mx3 + 5mx4 + 2mx5 + 15x + -20x4 + -15x + -8x5 = 15 + -15x + 8x3

Reorder the terms:
2mx3 + 5mx4 + 2mx5 + 15x + -15x + -20x4 + -8x5 = 15 + -15x + 8x3

Combine like terms: 15x + -15x = 0
2mx3 + 5mx4 + 2mx5 + 0 + -20x4 + -8x5 = 15 + -15x + 8x3
2mx3 + 5mx4 + 2mx5 + -20x4 + -8x5 = 15 + -15x + 8x3

Add '20x4' to each side of the equation.
2mx3 + 5mx4 + 2mx5 + -20x4 + 20x4 + -8x5 = 15 + -15x + 8x3 + 20x4

Combine like terms: -20x4 + 20x4 = 0
2mx3 + 5mx4 + 2mx5 + 0 + -8x5 = 15 + -15x + 8x3 + 20x4
2mx3 + 5mx4 + 2mx5 + -8x5 = 15 + -15x + 8x3 + 20x4

Add '8x5' to each side of the equation.
2mx3 + 5mx4 + 2mx5 + -8x5 + 8x5 = 15 + -15x + 8x3 + 20x4 + 8x5

Combine like terms: -8x5 + 8x5 = 0
2mx3 + 5mx4 + 2mx5 + 0 = 15 + -15x + 8x3 + 20x4 + 8x5
2mx3 + 5mx4 + 2mx5 = 15 + -15x + 8x3 + 20x4 + 8x5

Reorder the terms:
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 15 + -15x + 8x3 + 20x4 + 8x5 + -15 + 15x + -8x3 + -20x4 + -8x5

Reorder the terms:
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 15 + -15 + -15x + 15x + 8x3 + -8x3 + 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: 15 + -15 = 0
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 0 + -15x + 15x + 8x3 + -8x3 + 20x4 + -20x4 + 8x5 + -8x5
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = -15x + 15x + 8x3 + -8x3 + 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: -15x + 15x = 0
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 0 + 8x3 + -8x3 + 20x4 + -20x4 + 8x5 + -8x5
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 8x3 + -8x3 + 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: 8x3 + -8x3 = 0
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 0 + 20x4 + -20x4 + 8x5 + -8x5
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 20x4 + -20x4 + 8x5 + -8x5

Combine like terms: 20x4 + -20x4 = 0
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 0 + 8x5 + -8x5
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 8x5 + -8x5

Combine like terms: 8x5 + -8x5 = 0
-15 + 2mx3 + 5mx4 + 2mx5 + 15x + -8x3 + -20x4 + -8x5 = 0

The solution to this equation could not be determined.

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