10x^3(x-3)-5x(x-3)=5x(x-3)(2x^2-1)

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Solution for 10x^3(x-3)-5x(x-3)=5x(x-3)(2x^2-1) equation: 


Simplifying
10x3(x + -3) + -5x(x + -3) = 5x(x + -3)(2x2 + -1)

Reorder the terms:
10x3(-3 + x) + -5x(x + -3) = 5x(x + -3)(2x2 + -1)
(-3 * 10x3 + x * 10x3) + -5x(x + -3) = 5x(x + -3)(2x2 + -1)
(-30x3 + 10x4) + -5x(x + -3) = 5x(x + -3)(2x2 + -1)

Reorder the terms:
-30x3 + 10x4 + -5x(-3 + x) = 5x(x + -3)(2x2 + -1)
-30x3 + 10x4 + (-3 * -5x + x * -5x) = 5x(x + -3)(2x2 + -1)
-30x3 + 10x4 + (15x + -5x2) = 5x(x + -3)(2x2 + -1)

Reorder the terms:
15x + -5x2 + -30x3 + 10x4 = 5x(x + -3)(2x2 + -1)

Reorder the terms:
15x + -5x2 + -30x3 + 10x4 = 5x(-3 + x)(2x2 + -1)

Reorder the terms:
15x + -5x2 + -30x3 + 10x4 = 5x(-3 + x)(-1 + 2x2)

Multiply (-3 + x) * (-1 + 2x2)
15x + -5x2 + -30x3 + 10x4 = 5x(-3(-1 + 2x2) + x(-1 + 2x2))
15x + -5x2 + -30x3 + 10x4 = 5x((-1 * -3 + 2x2 * -3) + x(-1 + 2x2))
15x + -5x2 + -30x3 + 10x4 = 5x((3 + -6x2) + x(-1 + 2x2))
15x + -5x2 + -30x3 + 10x4 = 5x(3 + -6x2 + (-1 * x + 2x2 * x))
15x + -5x2 + -30x3 + 10x4 = 5x(3 + -6x2 + (-1x + 2x3))

Reorder the terms:
15x + -5x2 + -30x3 + 10x4 = 5x(3 + -1x + -6x2 + 2x3)
15x + -5x2 + -30x3 + 10x4 = 5x(3 + -1x + -6x2 + 2x3)
15x + -5x2 + -30x3 + 10x4 = (3 * 5x + -1x * 5x + -6x2 * 5x + 2x3 * 5x)
15x + -5x2 + -30x3 + 10x4 = (15x + -5x2 + -30x3 + 10x4)

Add '-15x' to each side of the equation.
15x + -5x2 + -30x3 + -15x + 10x4 = 15x + -5x2 + -30x3 + -15x + 10x4

Reorder the terms:
15x + -15x + -5x2 + -30x3 + 10x4 = 15x + -5x2 + -30x3 + -15x + 10x4

Combine like terms: 15x + -15x = 0
0 + -5x2 + -30x3 + 10x4 = 15x + -5x2 + -30x3 + -15x + 10x4
-5x2 + -30x3 + 10x4 = 15x + -5x2 + -30x3 + -15x + 10x4

Reorder the terms:
-5x2 + -30x3 + 10x4 = 15x + -15x + -5x2 + -30x3 + 10x4

Combine like terms: 15x + -15x = 0
-5x2 + -30x3 + 10x4 = 0 + -5x2 + -30x3 + 10x4
-5x2 + -30x3 + 10x4 = -5x2 + -30x3 + 10x4

Add '5x2' to each side of the equation.
-5x2 + -30x3 + 5x2 + 10x4 = -5x2 + -30x3 + 5x2 + 10x4

Reorder the terms:
-5x2 + 5x2 + -30x3 + 10x4 = -5x2 + -30x3 + 5x2 + 10x4

Combine like terms: -5x2 + 5x2 = 0
0 + -30x3 + 10x4 = -5x2 + -30x3 + 5x2 + 10x4
-30x3 + 10x4 = -5x2 + -30x3 + 5x2 + 10x4

Reorder the terms:
-30x3 + 10x4 = -5x2 + 5x2 + -30x3 + 10x4

Combine like terms: -5x2 + 5x2 = 0
-30x3 + 10x4 = 0 + -30x3 + 10x4
-30x3 + 10x4 = -30x3 + 10x4

Add '30x3' to each side of the equation.
-30x3 + 30x3 + 10x4 = -30x3 + 30x3 + 10x4

Combine like terms: -30x3 + 30x3 = 0
0 + 10x4 = -30x3 + 30x3 + 10x4
10x4 = -30x3 + 30x3 + 10x4

Combine like terms: -30x3 + 30x3 = 0
10x4 = 0 + 10x4
10x4 = 10x4

Add '-10x4' to each side of the equation.
10x4 + -10x4 = 10x4 + -10x4

Combine like terms: 10x4 + -10x4 = 0
0 = 10x4 + -10x4

Combine like terms: 10x4 + -10x4 = 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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