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

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Solution for x(x+4)(x-7)2=0 equation: 


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

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

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

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

Multiply (4 + x) * (-7 + x)
2x(4(-7 + x) + x(-7 + x)) = 0
2x((-7 * 4 + x * 4) + x(-7 + x)) = 0
2x((-28 + 4x) + x(-7 + x)) = 0
2x(-28 + 4x + (-7 * x + x * x)) = 0
2x(-28 + 4x + (-7x + x2)) = 0

Combine like terms: 4x + -7x = -3x
2x(-28 + -3x + x2) = 0
(-28 * 2x + -3x * 2x + x2 * 2x) = 0
(-56x + -6x2 + 2x3) = 0

Solving
-56x + -6x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-28 + -3x + x2) = 0

Factor a trinomial.
2x((-4 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

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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