x(12-2x)(20-2x)=x

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Solution for x(12-2x)(20-2x)=x equation:


Simplifying
x(12 + -2x)(20 + -2x) = x

Multiply (12 + -2x) * (20 + -2x)
x(12(20 + -2x) + -2x * (20 + -2x)) = x
x((20 * 12 + -2x * 12) + -2x * (20 + -2x)) = x
x((240 + -24x) + -2x * (20 + -2x)) = x
x(240 + -24x + (20 * -2x + -2x * -2x)) = x
x(240 + -24x + (-40x + 4x2)) = x

Combine like terms: -24x + -40x = -64x
x(240 + -64x + 4x2) = x
(240 * x + -64x * x + 4x2 * x) = x
(240x + -64x2 + 4x3) = x

Solving
240x + -64x2 + 4x3 = x

Solving for variable 'x'.

Reorder the terms:
240x + -1x + -64x2 + 4x3 = x + -1x

Combine like terms: 240x + -1x = 239x
239x + -64x2 + 4x3 = x + -1x

Combine like terms: x + -1x = 0
239x + -64x2 + 4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(239 + -64x + 4x2) = 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 '(239 + -64x + 4x2)' equal to zero and attempt to solve: Simplifying 239 + -64x + 4x2 = 0 Solving 239 + -64x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 59.75 + -16x + x2 = 0 Move the constant term to the right: Add '-59.75' to each side of the equation. 59.75 + -16x + -59.75 + x2 = 0 + -59.75 Reorder the terms: 59.75 + -59.75 + -16x + x2 = 0 + -59.75 Combine like terms: 59.75 + -59.75 = 0.00 0.00 + -16x + x2 = 0 + -59.75 -16x + x2 = 0 + -59.75 Combine like terms: 0 + -59.75 = -59.75 -16x + x2 = -59.75 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -59.75 + 64 Reorder the terms: 64 + -16x + x2 = -59.75 + 64 Combine like terms: -59.75 + 64 = 4.25 64 + -16x + x2 = 4.25 Factor a perfect square on the left side: (x + -8)(x + -8) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -8) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + -8 = 2.061552813 Simplifying x + -8 = 2.061552813 Reorder the terms: -8 + x = 2.061552813 Solving -8 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 2.061552813 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.061552813 + 8 x = 2.061552813 + 8 Combine like terms: 2.061552813 + 8 = 10.061552813 x = 10.061552813 Simplifying x = 10.061552813

Subproblem 2

x + -8 = -2.061552813 Simplifying x + -8 = -2.061552813 Reorder the terms: -8 + x = -2.061552813 Solving -8 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -2.061552813 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.061552813 + 8 x = -2.061552813 + 8 Combine like terms: -2.061552813 + 8 = 5.938447187 x = 5.938447187 Simplifying x = 5.938447187

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.061552813, 5.938447187}

Solution

x = {0, 10.061552813, 5.938447187}

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