(ax^3-3x^2+2bx-2)-(2x^3-cx^2-5x-4d)=x^2+x-6

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Solution for (ax^3-3x^2+2bx-2)-(2x^3-cx^2-5x-4d)=x^2+x-6 equation: 


Simplifying
(ax3 + -3x2 + 2bx + -2) + -1(2x3 + -1cx2 + -5x + -4d) = x2 + x + -6

Reorder the terms:
(-2 + ax3 + 2bx + -3x2) + -1(2x3 + -1cx2 + -5x + -4d) = x2 + x + -6

Remove parenthesis around (-2 + ax3 + 2bx + -3x2)
-2 + ax3 + 2bx + -3x2 + -1(2x3 + -1cx2 + -5x + -4d) = x2 + x + -6

Reorder the terms:
-2 + ax3 + 2bx + -3x2 + -1(-1cx2 + -4d + -5x + 2x3) = x2 + x + -6
-2 + ax3 + 2bx + -3x2 + (-1cx2 * -1 + -4d * -1 + -5x * -1 + 2x3 * -1) = x2 + x + -6
-2 + ax3 + 2bx + -3x2 + (1cx2 + 4d + 5x + -2x3) = x2 + x + -6

Reorder the terms:
-2 + ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = x2 + x + -6

Reorder the terms:
-2 + ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + x2

Solving
-2 + ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + x2

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + 2 + -2x3 = -6 + x + 2 + x2

Reorder the terms:
-2 + 2 + ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + 2 + x2

Combine like terms: -2 + 2 = 0
0 + ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + 2 + x2
ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -6 + x + 2 + x2

Reorder the terms:
ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -6 + 2 + x + x2

Combine like terms: -6 + 2 = -4
ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + x2

Add '-2bx' to each side of the equation.
ax3 + 2bx + 1cx2 + 4d + 5x + -3x2 + -2bx + -2x3 = -4 + x + -2bx + x2

Reorder the terms:
ax3 + 2bx + -2bx + 1cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + -2bx + x2

Combine like terms: 2bx + -2bx = 0
ax3 + 0 + 1cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + -2bx + x2
ax3 + 1cx2 + 4d + 5x + -3x2 + -2x3 = -4 + x + -2bx + x2

Reorder the terms:
ax3 + 1cx2 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + x2

Add '-1cx2' to each side of the equation.
ax3 + 1cx2 + 4d + 5x + -3x2 + -1cx2 + -2x3 = -4 + -2bx + x + -1cx2 + x2

Reorder the terms:
ax3 + 1cx2 + -1cx2 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + -1cx2 + x2

Combine like terms: 1cx2 + -1cx2 = 0
ax3 + 0 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + -1cx2 + x2
ax3 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + x + -1cx2 + x2

Reorder the terms:
ax3 + 4d + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + x2

Add '-4d' to each side of the equation.
ax3 + 4d + 5x + -3x2 + -4d + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2

Reorder the terms:
ax3 + 4d + -4d + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2

Combine like terms: 4d + -4d = 0
ax3 + 0 + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2
ax3 + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + x + -4d + x2

Reorder the terms:
ax3 + 5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + x2

Add '-5x' to each side of the equation.
ax3 + 5x + -3x2 + -5x + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2

Reorder the terms:
ax3 + 5x + -5x + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2

Combine like terms: 5x + -5x = 0
ax3 + 0 + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2
ax3 + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + x + -5x + x2

Combine like terms: x + -5x = -4x
ax3 + -3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2

Add '3x2' to each side of the equation.
ax3 + -3x2 + 3x2 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
ax3 + 0 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2 + 3x2
ax3 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + x2 + 3x2

Combine like terms: x2 + 3x2 = 4x2
ax3 + -2x3 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2

Add '2x3' to each side of the equation.
ax3 + -2x3 + 2x3 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2 + 2x3

Combine like terms: -2x3 + 2x3 = 0
ax3 + 0 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2 + 2x3
ax3 = -4 + -2bx + -1cx2 + -4d + -4x + 4x2 + 2x3

Divide each side by 'x3'.
a = -4x-3 + -2bx-2 + -1cx-1 + -4dx-3 + -4x-2 + 4x-1 + 2

Simplifying
a = -4x-3 + -2bx-2 + -1cx-1 + -4dx-3 + -4x-2 + 4x-1 + 2

Reorder the terms:
a = 2 + -2bx-2 + -1cx-1 + -4dx-3 + -4x-3 + -4x-2 + 4x-1

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