0=x(8-2x)(11-2x)

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Solution for 0=x(8-2x)(11-2x) equation:


Simplifying
0 = x(8 + -2x)(11 + -2x)

Multiply (8 + -2x) * (11 + -2x)
0 = x(8(11 + -2x) + -2x * (11 + -2x))
0 = x((11 * 8 + -2x * 8) + -2x * (11 + -2x))
0 = x((88 + -16x) + -2x * (11 + -2x))
0 = x(88 + -16x + (11 * -2x + -2x * -2x))
0 = x(88 + -16x + (-22x + 4x2))

Combine like terms: -16x + -22x = -38x
0 = x(88 + -38x + 4x2)
0 = (88 * x + -38x * x + 4x2 * x)
0 = (88x + -38x2 + 4x3)

Solving
0 = 88x + -38x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-88x + 38x2 + -4x3 = 88x + -38x2 + 4x3 + -88x + 38x2 + -4x3

Reorder the terms:
-88x + 38x2 + -4x3 = 88x + -88x + -38x2 + 38x2 + 4x3 + -4x3

Combine like terms: 88x + -88x = 0
-88x + 38x2 + -4x3 = 0 + -38x2 + 38x2 + 4x3 + -4x3
-88x + 38x2 + -4x3 = -38x2 + 38x2 + 4x3 + -4x3

Combine like terms: -38x2 + 38x2 = 0
-88x + 38x2 + -4x3 = 0 + 4x3 + -4x3
-88x + 38x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-88x + 38x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-44 + 19x + -2x2) = 0

Factor a trinomial.
2x((-11 + 2x)(4 + -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 '(-11 + 2x)' equal to zero and attempt to solve: Simplifying -11 + 2x = 0 Solving -11 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x = 0 + 11 2x = 0 + 11 Combine like terms: 0 + 11 = 11 2x = 11 Divide each side by '2'. x = 5.5 Simplifying x = 5.5

Subproblem 3

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

Solution

x = {0, 5.5, 4}

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