(mx^2+5)(2x^2+3x+4)-(8x^4+20x^3)=2x^4-5x^3+30x^2+15x+20

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Solution for (mx^2+5)(2x^2+3x+4)-(8x^4+20x^3)=2x^4-5x^3+30x^2+15x+20 equation: 


Simplifying
(mx2 + 5)(2x2 + 3x + 4) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20

Reorder the terms:
(5 + mx2)(2x2 + 3x + 4) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20

Reorder the terms:
(5 + mx2)(4 + 3x + 2x2) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20

Multiply (5 + mx2) * (4 + 3x + 2x2)
(5(4 + 3x + 2x2) + mx2(4 + 3x + 2x2)) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20
((4 * 5 + 3x * 5 + 2x2 * 5) + mx2(4 + 3x + 2x2)) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20
((20 + 15x + 10x2) + mx2(4 + 3x + 2x2)) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20
(20 + 15x + 10x2 + (4 * mx2 + 3x * mx2 + 2x2 * mx2)) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20
(20 + 15x + 10x2 + (4mx2 + 3mx3 + 2mx4)) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20

Reorder the terms:
(20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20
(20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2) + -1(8x4 + 20x3) = 2x4 + -5x3 + 30x2 + 15x + 20

Reorder the terms:
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -1(20x3 + 8x4) = 2x4 + -5x3 + 30x2 + 15x + 20
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + (20x3 * -1 + 8x4 * -1) = 2x4 + -5x3 + 30x2 + 15x + 20
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + (-20x3 + -8x4) = 2x4 + -5x3 + 30x2 + 15x + 20

Reorder the terms:
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 20 + 15x + 30x2 + -5x3 + 2x4

Add '-20' to each side of the equation.
20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -20 + -8x4 = 20 + 15x + 30x2 + -5x3 + -20 + 2x4

Reorder the terms:
20 + -20 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 20 + 15x + 30x2 + -5x3 + -20 + 2x4

Combine like terms: 20 + -20 = 0
0 + 4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 20 + 15x + 30x2 + -5x3 + -20 + 2x4
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 20 + 15x + 30x2 + -5x3 + -20 + 2x4

Reorder the terms:
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 20 + -20 + 15x + 30x2 + -5x3 + 2x4

Combine like terms: 20 + -20 = 0
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 0 + 15x + 30x2 + -5x3 + 2x4
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -8x4 = 15x + 30x2 + -5x3 + 2x4

Add '-15x' to each side of the equation.
4mx2 + 3mx3 + 2mx4 + 15x + 10x2 + -20x3 + -15x + -8x4 = 15x + 30x2 + -5x3 + -15x + 2x4

Reorder the terms:
4mx2 + 3mx3 + 2mx4 + 15x + -15x + 10x2 + -20x3 + -8x4 = 15x + 30x2 + -5x3 + -15x + 2x4

Combine like terms: 15x + -15x = 0
4mx2 + 3mx3 + 2mx4 + 0 + 10x2 + -20x3 + -8x4 = 15x + 30x2 + -5x3 + -15x + 2x4
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -8x4 = 15x + 30x2 + -5x3 + -15x + 2x4

Reorder the terms:
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -8x4 = 15x + -15x + 30x2 + -5x3 + 2x4

Combine like terms: 15x + -15x = 0
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -8x4 = 0 + 30x2 + -5x3 + 2x4
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -8x4 = 30x2 + -5x3 + 2x4

Solving
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -8x4 = 30x2 + -5x3 + 2x4

Solving for variable 'm'.

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

Add '-10x2' to each side of the equation.
4mx2 + 3mx3 + 2mx4 + 10x2 + -20x3 + -10x2 + -8x4 = 30x2 + -5x3 + -10x2 + 2x4

Reorder the terms:
4mx2 + 3mx3 + 2mx4 + 10x2 + -10x2 + -20x3 + -8x4 = 30x2 + -5x3 + -10x2 + 2x4

Combine like terms: 10x2 + -10x2 = 0
4mx2 + 3mx3 + 2mx4 + 0 + -20x3 + -8x4 = 30x2 + -5x3 + -10x2 + 2x4
4mx2 + 3mx3 + 2mx4 + -20x3 + -8x4 = 30x2 + -5x3 + -10x2 + 2x4

Reorder the terms:
4mx2 + 3mx3 + 2mx4 + -20x3 + -8x4 = 30x2 + -10x2 + -5x3 + 2x4

Combine like terms: 30x2 + -10x2 = 20x2
4mx2 + 3mx3 + 2mx4 + -20x3 + -8x4 = 20x2 + -5x3 + 2x4

Add '20x3' to each side of the equation.
4mx2 + 3mx3 + 2mx4 + -20x3 + 20x3 + -8x4 = 20x2 + -5x3 + 20x3 + 2x4

Combine like terms: -20x3 + 20x3 = 0
4mx2 + 3mx3 + 2mx4 + 0 + -8x4 = 20x2 + -5x3 + 20x3 + 2x4
4mx2 + 3mx3 + 2mx4 + -8x4 = 20x2 + -5x3 + 20x3 + 2x4

Combine like terms: -5x3 + 20x3 = 15x3
4mx2 + 3mx3 + 2mx4 + -8x4 = 20x2 + 15x3 + 2x4

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4m + 3mx + 2mx2 + -20 + -15x + -10x2) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 = 0 + -1x2
Remove the zero:
0 = -1x2

Simplifying
0 = -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4m + 3mx + 2mx2 + -20 + -15x + -10x2)' equal to zero and attempt to solve:

Simplifying
4m + 3mx + 2mx2 + -20 + -15x + -10x2 = 0

Reorder the terms:
-20 + 4m + 3mx + 2mx2 + -15x + -10x2 = 0

Solving
-20 + 4m + 3mx + 2mx2 + -15x + -10x2 = 0

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

Add '20' to each side of the equation.
-20 + 4m + 3mx + 2mx2 + -15x + 20 + -10x2 = 0 + 20

Reorder the terms:
-20 + 20 + 4m + 3mx + 2mx2 + -15x + -10x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 4m + 3mx + 2mx2 + -15x + -10x2 = 0 + 20
4m + 3mx + 2mx2 + -15x + -10x2 = 0 + 20

Combine like terms: 0 + 20 = 20
4m + 3mx + 2mx2 + -15x + -10x2 = 20

Add '15x' to each side of the equation.
4m + 3mx + 2mx2 + -15x + 15x + -10x2 = 20 + 15x

Combine like terms: -15x + 15x = 0
4m + 3mx + 2mx2 + 0 + -10x2 = 20 + 15x
4m + 3mx + 2mx2 + -10x2 = 20 + 15x

Add '10x2' to each side of the equation.
4m + 3mx + 2mx2 + -10x2 + 10x2 = 20 + 15x + 10x2

Combine like terms: -10x2 + 10x2 = 0
4m + 3mx + 2mx2 + 0 = 20 + 15x + 10x2
4m + 3mx + 2mx2 = 20 + 15x + 10x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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