462=(X+6)(X-4)(2)

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Solution for 462=(X+6)(X-4)(2) equation: 


Simplifying
462 = (X + 6)(X + -4)(2)

Reorder the terms:
462 = (6 + X)(X + -4)(2)

Reorder the terms:
462 = (6 + X)(-4 + X)(2)

Reorder the terms for easier multiplication:
462 = 2(6 + X)(-4 + X)

Multiply (6 + X) * (-4 + X)
462 = 2(6(-4 + X) + X(-4 + X))
462 = 2((-4 * 6 + X * 6) + X(-4 + X))
462 = 2((-24 + 6X) + X(-4 + X))
462 = 2(-24 + 6X + (-4 * X + X * X))
462 = 2(-24 + 6X + (-4X + X2))

Combine like terms: 6X + -4X = 2X
462 = 2(-24 + 2X + X2)
462 = (-24 * 2 + 2X * 2 + X2 * 2)
462 = (-48 + 4X + 2X2)

Solving
462 = -48 + 4X + 2X2

Solving for variable 'X'.

Combine like terms: 462 + 48 = 510
510 + -4X + -2X2 = -48 + 4X + 2X2 + 48 + -4X + -2X2

Reorder the terms:
510 + -4X + -2X2 = -48 + 48 + 4X + -4X + 2X2 + -2X2

Combine like terms: -48 + 48 = 0
510 + -4X + -2X2 = 0 + 4X + -4X + 2X2 + -2X2
510 + -4X + -2X2 = 4X + -4X + 2X2 + -2X2

Combine like terms: 4X + -4X = 0
510 + -4X + -2X2 = 0 + 2X2 + -2X2
510 + -4X + -2X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
510 + -4X + -2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(255 + -2X + -1X2) = 0

Factor a trinomial.
2((15 + -1X)(17 + X)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + -1X)' equal to zero and attempt to solve:

Simplifying
15 + -1X = 0

Solving
15 + -1X = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1X = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1X = 0 + -15
-1X = 0 + -15

Combine like terms: 0 + -15 = -15
-1X = -15

Divide each side by '-1'.
X = 15

Simplifying
X = 15

Subproblem 2
Set the factor '(17 + X)' equal to zero and attempt to solve:

Simplifying
17 + X = 0

Solving
17 + X = 0

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

Add '-17' to each side of the equation.
17 + -17 + X = 0 + -17

Combine like terms: 17 + -17 = 0
0 + X = 0 + -17
X = 0 + -17

Combine like terms: 0 + -17 = -17
X = -17

Simplifying
X = -17
Solution
X = {15, -17}

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