(3x-1)(x+5)(4x-3)=12x^3+47x^2-62x+15

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Solution for (3x-1)(x+5)(4x-3)=12x^3+47x^2-62x+15 equation: 


Simplifying
(3x + -1)(x + 5)(4x + -3) = 12x3 + 47x2 + -62x + 15

Reorder the terms:
(-1 + 3x)(x + 5)(4x + -3) = 12x3 + 47x2 + -62x + 15

Reorder the terms:
(-1 + 3x)(5 + x)(4x + -3) = 12x3 + 47x2 + -62x + 15

Reorder the terms:
(-1 + 3x)(5 + x)(-3 + 4x) = 12x3 + 47x2 + -62x + 15

Multiply (-1 + 3x) * (5 + x)
(-1(5 + x) + 3x * (5 + x))(-3 + 4x) = 12x3 + 47x2 + -62x + 15
((5 * -1 + x * -1) + 3x * (5 + x))(-3 + 4x) = 12x3 + 47x2 + -62x + 15
((-5 + -1x) + 3x * (5 + x))(-3 + 4x) = 12x3 + 47x2 + -62x + 15
(-5 + -1x + (5 * 3x + x * 3x))(-3 + 4x) = 12x3 + 47x2 + -62x + 15
(-5 + -1x + (15x + 3x2))(-3 + 4x) = 12x3 + 47x2 + -62x + 15

Combine like terms: -1x + 15x = 14x
(-5 + 14x + 3x2)(-3 + 4x) = 12x3 + 47x2 + -62x + 15

Multiply (-5 + 14x + 3x2) * (-3 + 4x)
(-5(-3 + 4x) + 14x * (-3 + 4x) + 3x2 * (-3 + 4x)) = 12x3 + 47x2 + -62x + 15
((-3 * -5 + 4x * -5) + 14x * (-3 + 4x) + 3x2 * (-3 + 4x)) = 12x3 + 47x2 + -62x + 15
((15 + -20x) + 14x * (-3 + 4x) + 3x2 * (-3 + 4x)) = 12x3 + 47x2 + -62x + 15
(15 + -20x + (-3 * 14x + 4x * 14x) + 3x2 * (-3 + 4x)) = 12x3 + 47x2 + -62x + 15
(15 + -20x + (-42x + 56x2) + 3x2 * (-3 + 4x)) = 12x3 + 47x2 + -62x + 15
(15 + -20x + -42x + 56x2 + (-3 * 3x2 + 4x * 3x2)) = 12x3 + 47x2 + -62x + 15
(15 + -20x + -42x + 56x2 + (-9x2 + 12x3)) = 12x3 + 47x2 + -62x + 15

Combine like terms: -20x + -42x = -62x
(15 + -62x + 56x2 + -9x2 + 12x3) = 12x3 + 47x2 + -62x + 15

Combine like terms: 56x2 + -9x2 = 47x2
(15 + -62x + 47x2 + 12x3) = 12x3 + 47x2 + -62x + 15

Reorder the terms:
15 + -62x + 47x2 + 12x3 = 15 + -62x + 47x2 + 12x3

Add '-15' to each side of the equation.
15 + -62x + 47x2 + -15 + 12x3 = 15 + -62x + 47x2 + -15 + 12x3

Reorder the terms:
15 + -15 + -62x + 47x2 + 12x3 = 15 + -62x + 47x2 + -15 + 12x3

Combine like terms: 15 + -15 = 0
0 + -62x + 47x2 + 12x3 = 15 + -62x + 47x2 + -15 + 12x3
-62x + 47x2 + 12x3 = 15 + -62x + 47x2 + -15 + 12x3

Reorder the terms:
-62x + 47x2 + 12x3 = 15 + -15 + -62x + 47x2 + 12x3

Combine like terms: 15 + -15 = 0
-62x + 47x2 + 12x3 = 0 + -62x + 47x2 + 12x3
-62x + 47x2 + 12x3 = -62x + 47x2 + 12x3

Add '62x' to each side of the equation.
-62x + 47x2 + 62x + 12x3 = -62x + 47x2 + 62x + 12x3

Reorder the terms:
-62x + 62x + 47x2 + 12x3 = -62x + 47x2 + 62x + 12x3

Combine like terms: -62x + 62x = 0
0 + 47x2 + 12x3 = -62x + 47x2 + 62x + 12x3
47x2 + 12x3 = -62x + 47x2 + 62x + 12x3

Reorder the terms:
47x2 + 12x3 = -62x + 62x + 47x2 + 12x3

Combine like terms: -62x + 62x = 0
47x2 + 12x3 = 0 + 47x2 + 12x3
47x2 + 12x3 = 47x2 + 12x3

Add '-47x2' to each side of the equation.
47x2 + -47x2 + 12x3 = 47x2 + -47x2 + 12x3

Combine like terms: 47x2 + -47x2 = 0
0 + 12x3 = 47x2 + -47x2 + 12x3
12x3 = 47x2 + -47x2 + 12x3

Combine like terms: 47x2 + -47x2 = 0
12x3 = 0 + 12x3
12x3 = 12x3

Add '-12x3' to each side of the equation.
12x3 + -12x3 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 0
0 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 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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