(x-3)(x+5)(x-4)=(x-3)(x+5)(x-4)

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Solution for (x-3)(x+5)(x-4)=(x-3)(x+5)(x-4) equation: 


Simplifying
(x + -3)(x + 5)(x + -4) = (x + -3)(x + 5)(x + -4)

Reorder the terms:
(-3 + x)(x + 5)(x + -4) = (x + -3)(x + 5)(x + -4)

Reorder the terms:
(-3 + x)(5 + x)(x + -4) = (x + -3)(x + 5)(x + -4)

Reorder the terms:
(-3 + x)(5 + x)(-4 + x) = (x + -3)(x + 5)(x + -4)

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x))(-4 + x) = (x + -3)(x + 5)(x + -4)
((5 * -3 + x * -3) + x(5 + x))(-4 + x) = (x + -3)(x + 5)(x + -4)
((-15 + -3x) + x(5 + x))(-4 + x) = (x + -3)(x + 5)(x + -4)
(-15 + -3x + (5 * x + x * x))(-4 + x) = (x + -3)(x + 5)(x + -4)
(-15 + -3x + (5x + x2))(-4 + x) = (x + -3)(x + 5)(x + -4)

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2)(-4 + x) = (x + -3)(x + 5)(x + -4)

Multiply (-15 + 2x + x2) * (-4 + x)
(-15(-4 + x) + 2x * (-4 + x) + x2(-4 + x)) = (x + -3)(x + 5)(x + -4)
((-4 * -15 + x * -15) + 2x * (-4 + x) + x2(-4 + x)) = (x + -3)(x + 5)(x + -4)
((60 + -15x) + 2x * (-4 + x) + x2(-4 + x)) = (x + -3)(x + 5)(x + -4)
(60 + -15x + (-4 * 2x + x * 2x) + x2(-4 + x)) = (x + -3)(x + 5)(x + -4)
(60 + -15x + (-8x + 2x2) + x2(-4 + x)) = (x + -3)(x + 5)(x + -4)
(60 + -15x + -8x + 2x2 + (-4 * x2 + x * x2)) = (x + -3)(x + 5)(x + -4)
(60 + -15x + -8x + 2x2 + (-4x2 + x3)) = (x + -3)(x + 5)(x + -4)

Combine like terms: -15x + -8x = -23x
(60 + -23x + 2x2 + -4x2 + x3) = (x + -3)(x + 5)(x + -4)

Combine like terms: 2x2 + -4x2 = -2x2
(60 + -23x + -2x2 + x3) = (x + -3)(x + 5)(x + -4)

Reorder the terms:
60 + -23x + -2x2 + x3 = (-3 + x)(x + 5)(x + -4)

Reorder the terms:
60 + -23x + -2x2 + x3 = (-3 + x)(5 + x)(x + -4)

Reorder the terms:
60 + -23x + -2x2 + x3 = (-3 + x)(5 + x)(-4 + x)

Multiply (-3 + x) * (5 + x)
60 + -23x + -2x2 + x3 = (-3(5 + x) + x(5 + x))(-4 + x)
60 + -23x + -2x2 + x3 = ((5 * -3 + x * -3) + x(5 + x))(-4 + x)
60 + -23x + -2x2 + x3 = ((-15 + -3x) + x(5 + x))(-4 + x)
60 + -23x + -2x2 + x3 = (-15 + -3x + (5 * x + x * x))(-4 + x)
60 + -23x + -2x2 + x3 = (-15 + -3x + (5x + x2))(-4 + x)

Combine like terms: -3x + 5x = 2x
60 + -23x + -2x2 + x3 = (-15 + 2x + x2)(-4 + x)

Multiply (-15 + 2x + x2) * (-4 + x)
60 + -23x + -2x2 + x3 = (-15(-4 + x) + 2x * (-4 + x) + x2(-4 + x))
60 + -23x + -2x2 + x3 = ((-4 * -15 + x * -15) + 2x * (-4 + x) + x2(-4 + x))
60 + -23x + -2x2 + x3 = ((60 + -15x) + 2x * (-4 + x) + x2(-4 + x))
60 + -23x + -2x2 + x3 = (60 + -15x + (-4 * 2x + x * 2x) + x2(-4 + x))
60 + -23x + -2x2 + x3 = (60 + -15x + (-8x + 2x2) + x2(-4 + x))
60 + -23x + -2x2 + x3 = (60 + -15x + -8x + 2x2 + (-4 * x2 + x * x2))
60 + -23x + -2x2 + x3 = (60 + -15x + -8x + 2x2 + (-4x2 + x3))

Combine like terms: -15x + -8x = -23x
60 + -23x + -2x2 + x3 = (60 + -23x + 2x2 + -4x2 + x3)

Combine like terms: 2x2 + -4x2 = -2x2
60 + -23x + -2x2 + x3 = (60 + -23x + -2x2 + x3)

Add '-60' to each side of the equation.
60 + -23x + -2x2 + -60 + x3 = 60 + -23x + -2x2 + -60 + x3

Reorder the terms:
60 + -60 + -23x + -2x2 + x3 = 60 + -23x + -2x2 + -60 + x3

Combine like terms: 60 + -60 = 0
0 + -23x + -2x2 + x3 = 60 + -23x + -2x2 + -60 + x3
-23x + -2x2 + x3 = 60 + -23x + -2x2 + -60 + x3

Reorder the terms:
-23x + -2x2 + x3 = 60 + -60 + -23x + -2x2 + x3

Combine like terms: 60 + -60 = 0
-23x + -2x2 + x3 = 0 + -23x + -2x2 + x3
-23x + -2x2 + x3 = -23x + -2x2 + x3

Add '23x' to each side of the equation.
-23x + -2x2 + 23x + x3 = -23x + -2x2 + 23x + x3

Reorder the terms:
-23x + 23x + -2x2 + x3 = -23x + -2x2 + 23x + x3

Combine like terms: -23x + 23x = 0
0 + -2x2 + x3 = -23x + -2x2 + 23x + x3
-2x2 + x3 = -23x + -2x2 + 23x + x3

Reorder the terms:
-2x2 + x3 = -23x + 23x + -2x2 + x3

Combine like terms: -23x + 23x = 0
-2x2 + x3 = 0 + -2x2 + x3
-2x2 + x3 = -2x2 + x3

Add '2x2' to each side of the equation.
-2x2 + 2x2 + x3 = -2x2 + 2x2 + x3

Combine like terms: -2x2 + 2x2 = 0
0 + x3 = -2x2 + 2x2 + x3
x3 = -2x2 + 2x2 + x3

Combine like terms: -2x2 + 2x2 = 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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