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

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


Simplifying
(mx2 + 5)(2x2 + 3x + 4) + -1(8x4 + 20x3) = 0

Reorder the terms:
(5 + mx2)(2x2 + 3x + 4) + -1(8x4 + 20x3) = 0

Reorder the terms:
(5 + mx2)(4 + 3x + 2x2) + -1(8x4 + 20x3) = 0

Multiply (5 + mx2) * (4 + 3x + 2x2)
(5(4 + 3x + 2x2) + mx2(4 + 3x + 2x2)) + -1(8x4 + 20x3) = 0
((4 * 5 + 3x * 5 + 2x2 * 5) + mx2(4 + 3x + 2x2)) + -1(8x4 + 20x3) = 0
((20 + 15x + 10x2) + mx2(4 + 3x + 2x2)) + -1(8x4 + 20x3) = 0
(20 + 15x + 10x2 + (4 * mx2 + 3x * mx2 + 2x2 * mx2)) + -1(8x4 + 20x3) = 0
(20 + 15x + 10x2 + (4mx2 + 3mx3 + 2mx4)) + -1(8x4 + 20x3) = 0

Reorder the terms:
(20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2) + -1(8x4 + 20x3) = 0
(20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2) + -1(8x4 + 20x3) = 0

Reorder the terms:
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -1(20x3 + 8x4) = 0
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + (20x3 * -1 + 8x4 * -1) = 0
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + (-20x3 + -8x4) = 0

Solving
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0

Solving for variable 'm'.

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

Add '-20' to each side of the equation.
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -20 + -8x4 = 0 + -20

Reorder the terms:
20 + -20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + -20
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + -20

Combine like terms: 0 + -20 = -20
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = -20

Add '-15x' to each side of the equation.
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -15x + -8x4 = -20 + -15x

Reorder the terms:
4mx2 + 3mx3 + 2mx4 + 15x + -15x + 10x2 + -20x3 + -8x4 = -20 + -15x

Combine like terms: 15x + -15x = 0
4mx2 + 3mx3 + 2mx4 + 0 + 10x2 + -20x3 + -8x4 = -20 + -15x
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -8x4 = -20 + -15x

Add '-10x2' to each side of the equation.
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -10x2 + -8x4 = -20 + -15x + -10x2

Reorder the terms:
4mx2 + 3mx3 + 2mx4 + 10x2 + -10x2 + -20x3 + -8x4 = -20 + -15x + -10x2

Combine like terms: 10x2 + -10x2 = 0
4mx2 + 3mx3 + 2mx4 + 0 + -20x3 + -8x4 = -20 + -15x + -10x2
4mx2 + 3mx3 + 2mx4 + -20x3 + -8x4 = -20 + -15x + -10x2

Add '20x3' to each side of the equation.
4mx2 + 3mx3 + 2mx4 + -20x3 + 20x3 + -8x4 = -20 + -15x + -10x2 + 20x3

Combine like terms: -20x3 + 20x3 = 0
4mx2 + 3mx3 + 2mx4 + 0 + -8x4 = -20 + -15x + -10x2 + 20x3
4mx2 + 3mx3 + 2mx4 + -8x4 = -20 + -15x + -10x2 + 20x3

Add '8x4' to each side of the equation.
4mx2 + 3mx3 + 2mx4 + -8x4 + 8x4 = -20 + -15x + -10x2 + 20x3 + 8x4

Combine like terms: -8x4 + 8x4 = 0
4mx2 + 3mx3 + 2mx4 + 0 = -20 + -15x + -10x2 + 20x3 + 8x4
4mx2 + 3mx3 + 2mx4 = -20 + -15x + -10x2 + 20x3 + 8x4

Reorder the terms:
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = -20 + -15x + -10x2 + 20x3 + 8x4 + 20 + 15x + 10x2 + -20x3 + -8x4

Reorder the terms:
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = -20 + 20 + -15x + 15x + -10x2 + 10x2 + 20x3 + -20x3 + 8x4 + -8x4

Combine like terms: -20 + 20 = 0
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + -15x + 15x + -10x2 + 10x2 + 20x3 + -20x3 + 8x4 + -8x4
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = -15x + 15x + -10x2 + 10x2 + 20x3 + -20x3 + 8x4 + -8x4

Combine like terms: -15x + 15x = 0
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + -10x2 + 10x2 + 20x3 + -20x3 + 8x4 + -8x4
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = -10x2 + 10x2 + 20x3 + -20x3 + 8x4 + -8x4

Combine like terms: -10x2 + 10x2 = 0
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + 20x3 + -20x3 + 8x4 + -8x4
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 20x3 + -20x3 + 8x4 + -8x4

Combine like terms: 20x3 + -20x3 = 0
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + 8x4 + -8x4
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 8x4 + -8x4

Combine like terms: 8x4 + -8x4 = 0
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0

The solution to this equation could not be determined.

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