(X-5)x(3x+6)=0

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Solution for (X-5)x(3x+6)=0 equation:


Simplifying
(X + -5) * x(3x + 6) = 0

Reorder the terms:
(-5 + X) * x(3x + 6) = 0

Reorder the terms:
(-5 + X) * x(6 + 3x) = 0

Reorder the terms for easier multiplication:
x(-5 + X)(6 + 3x) = 0

Multiply (-5 + X) * (6 + 3x)
x(-5(6 + 3x) + X(6 + 3x)) = 0
x((6 * -5 + 3x * -5) + X(6 + 3x)) = 0
x((-30 + -15x) + X(6 + 3x)) = 0
x(-30 + -15x + (6 * X + 3x * X)) = 0
x(-30 + -15x + (6X + 3xX)) = 0

Reorder the terms:
x(-30 + 6X + -15x + 3xX) = 0
x(-30 + 6X + -15x + 3xX) = 0
(-30 * x + 6X * x + -15x * x + 3xX * x) = 0
(-30x + 6xX + -15x2 + 3x2X) = 0

Solving
-30x + 6xX + -15x2 + 3x2X = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-10 + 2X + -5x + xX) = 0

Ignore the factor 3.

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 '(-10 + 2X + -5x + xX)' equal to zero and attempt to solve: Simplifying -10 + 2X + -5x + xX = 0 Solving -10 + 2X + -5x + xX = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 2X + -5x + 10 + xX = 0 + 10 Reorder the terms: -10 + 10 + 2X + -5x + xX = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2X + -5x + xX = 0 + 10 2X + -5x + xX = 0 + 10 Combine like terms: 0 + 10 = 10 2X + -5x + xX = 10 Add '-2X' to each side of the equation. 2X + -5x + -2X + xX = 10 + -2X Reorder the terms: 2X + -2X + -5x + xX = 10 + -2X Combine like terms: 2X + -2X = 0 0 + -5x + xX = 10 + -2X -5x + xX = 10 + -2X The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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