(x-6)(x^2+3x+5)=x^3+3x^2+5x-6x^2-18x-30

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Solution for (x-6)(x^2+3x+5)=x^3+3x^2+5x-6x^2-18x-30 equation: 


Simplifying
(x + -6)(x2 + 3x + 5) = x3 + 3x2 + 5x + -6x2 + -18x + -30

Reorder the terms:
(-6 + x)(x2 + 3x + 5) = x3 + 3x2 + 5x + -6x2 + -18x + -30

Reorder the terms:
(-6 + x)(5 + 3x + x2) = x3 + 3x2 + 5x + -6x2 + -18x + -30

Multiply (-6 + x) * (5 + 3x + x2)
(-6(5 + 3x + x2) + x(5 + 3x + x2)) = x3 + 3x2 + 5x + -6x2 + -18x + -30
((5 * -6 + 3x * -6 + x2 * -6) + x(5 + 3x + x2)) = x3 + 3x2 + 5x + -6x2 + -18x + -30
((-30 + -18x + -6x2) + x(5 + 3x + x2)) = x3 + 3x2 + 5x + -6x2 + -18x + -30
(-30 + -18x + -6x2 + (5 * x + 3x * x + x2 * x)) = x3 + 3x2 + 5x + -6x2 + -18x + -30
(-30 + -18x + -6x2 + (5x + 3x2 + x3)) = x3 + 3x2 + 5x + -6x2 + -18x + -30

Reorder the terms:
(-30 + -18x + 5x + -6x2 + 3x2 + x3) = x3 + 3x2 + 5x + -6x2 + -18x + -30

Combine like terms: -18x + 5x = -13x
(-30 + -13x + -6x2 + 3x2 + x3) = x3 + 3x2 + 5x + -6x2 + -18x + -30

Combine like terms: -6x2 + 3x2 = -3x2
(-30 + -13x + -3x2 + x3) = x3 + 3x2 + 5x + -6x2 + -18x + -30

Reorder the terms:
-30 + -13x + -3x2 + x3 = -30 + 5x + -18x + 3x2 + -6x2 + x3

Combine like terms: 5x + -18x = -13x
-30 + -13x + -3x2 + x3 = -30 + -13x + 3x2 + -6x2 + x3

Combine like terms: 3x2 + -6x2 = -3x2
-30 + -13x + -3x2 + x3 = -30 + -13x + -3x2 + x3

Add '30' to each side of the equation.
-30 + -13x + -3x2 + 30 + x3 = -30 + -13x + -3x2 + 30 + x3

Reorder the terms:
-30 + 30 + -13x + -3x2 + x3 = -30 + -13x + -3x2 + 30 + x3

Combine like terms: -30 + 30 = 0
0 + -13x + -3x2 + x3 = -30 + -13x + -3x2 + 30 + x3
-13x + -3x2 + x3 = -30 + -13x + -3x2 + 30 + x3

Reorder the terms:
-13x + -3x2 + x3 = -30 + 30 + -13x + -3x2 + x3

Combine like terms: -30 + 30 = 0
-13x + -3x2 + x3 = 0 + -13x + -3x2 + x3
-13x + -3x2 + x3 = -13x + -3x2 + x3

Add '13x' to each side of the equation.
-13x + -3x2 + 13x + x3 = -13x + -3x2 + 13x + x3

Reorder the terms:
-13x + 13x + -3x2 + x3 = -13x + -3x2 + 13x + x3

Combine like terms: -13x + 13x = 0
0 + -3x2 + x3 = -13x + -3x2 + 13x + x3
-3x2 + x3 = -13x + -3x2 + 13x + x3

Reorder the terms:
-3x2 + x3 = -13x + 13x + -3x2 + x3

Combine like terms: -13x + 13x = 0
-3x2 + x3 = 0 + -3x2 + x3
-3x2 + x3 = -3x2 + x3

Add '3x2' to each side of the equation.
-3x2 + 3x2 + x3 = -3x2 + 3x2 + x3

Combine like terms: -3x2 + 3x2 = 0
0 + x3 = -3x2 + 3x2 + x3
x3 = -3x2 + 3x2 + x3

Combine like terms: -3x2 + 3x2 = 0
x3 = 0 + x3
x3 = x3

Add '-1x3' to each side of the equation.
x3 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
0 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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