x(x+6)(x-9)=0

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Solution for x(x+6)(x-9)=0 equation:


Simplifying
x(x + 6)(x + -9) = 0

Reorder the terms:
x(6 + x)(x + -9) = 0

Reorder the terms:
x(6 + x)(-9 + x) = 0

Multiply (6 + x) * (-9 + x)
x(6(-9 + x) + x(-9 + x)) = 0
x((-9 * 6 + x * 6) + x(-9 + x)) = 0
x((-54 + 6x) + x(-9 + x)) = 0
x(-54 + 6x + (-9 * x + x * x)) = 0
x(-54 + 6x + (-9x + x2)) = 0

Combine like terms: 6x + -9x = -3x
x(-54 + -3x + x2) = 0
(-54 * x + -3x * x + x2 * x) = 0
(-54x + -3x2 + x3) = 0

Solving
-54x + -3x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-54 + -3x + x2) = 0

Factor a trinomial.
x((-6 + -1x)(9 + -1x)) = 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 '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 3

Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {0, -6, 9}

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