[x-7]x[x-4]=0

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Solution for [x-7]x[x-4]=0 equation: 


Simplifying
[x + -7] * x[x + -4] = 0

Reorder the terms:
[-7 + x] * x[x + -4] = 0

Reorder the terms:
[-7 + x] * x[-4 + x] = 0

Reorder the terms for easier multiplication:
x[-7 + x][-4 + x] = 0

Multiply [-7 + x] * [-4 + x]
x[-7[-4 + x] + x[-4 + x]] = 0
x[[-4 * -7 + x * -7] + x[-4 + x]] = 0
x[[28 + -7x] + x[-4 + x]] = 0
x[28 + -7x + [-4 * x + x * x]] = 0
x[28 + -7x + [-4x + x2]] = 0

Combine like terms: -7x + -4x = -11x
x[28 + -11x + x2] = 0
[28 * x + -11x * x + x2 * x] = 0
[28x + -11x2 + x3] = 0

Solving
28x + -11x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(28 + -11x + x2) = 0

Factor a trinomial.
x((4 + -1x)(7 + -1x)) = 0


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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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, 4, 7}

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