3x=x(1-(x-3))

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Solution for 3x=x(1-(x-3)) equation:


Simplifying
3x = x(1 + -1(x + -3))

Reorder the terms:
3x = x(1 + -1(-3 + x))
3x = x(1 + (-3 * -1 + x * -1))
3x = x(1 + (3 + -1x))

Combine like terms: 1 + 3 = 4
3x = x(4 + -1x)
3x = (4 * x + -1x * x)
3x = (4x + -1x2)

Solving
3x = 4x + -1x2

Solving for variable 'x'.

Combine like terms: 3x + -4x = -1x
-1x + x2 = 4x + -1x2 + -4x + x2

Reorder the terms:
-1x + x2 = 4x + -4x + -1x2 + x2

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

Combine like terms: -1x2 + x2 = 0
-1x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x) = 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1

Solution

x = {0, 1}

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