3(x-7)(x-2)(4x)=

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Solution for 3(x-7)(x-2)(4x)= equation:


Simplifying
3(x + -7)(x + -2)(4x) = 0

Reorder the terms:
3(-7 + x)(x + -2)(4x) = 0

Reorder the terms:
3(-7 + x)(-2 + x)(4x) = 0

Remove parenthesis around (4x)
3(-7 + x)(-2 + x) * 4x = 0

Reorder the terms for easier multiplication:
3 * 4x(-7 + x)(-2 + x) = 0

Multiply 3 * 4
12x(-7 + x)(-2 + x) = 0

Multiply (-7 + x) * (-2 + x)
12x(-7(-2 + x) + x(-2 + x)) = 0
12x((-2 * -7 + x * -7) + x(-2 + x)) = 0
12x((14 + -7x) + x(-2 + x)) = 0
12x(14 + -7x + (-2 * x + x * x)) = 0
12x(14 + -7x + (-2x + x2)) = 0

Combine like terms: -7x + -2x = -9x
12x(14 + -9x + x2) = 0
(14 * 12x + -9x * 12x + x2 * 12x) = 0
(168x + -108x2 + 12x3) = 0

Solving
168x + -108x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(14 + -9x + x2) = 0

Factor a trinomial.
12x((2 + -1x)(7 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 2, 7}

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