(x-6)(x+6)(x^2-36)=

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Solution for (x-6)(x+6)(x^2-36)= equation:


Simplifying
(x + -6)(x + 6)(x2 + -36) = 0

Reorder the terms:
(-6 + x)(x + 6)(x2 + -36) = 0

Reorder the terms:
(-6 + x)(6 + x)(x2 + -36) = 0

Reorder the terms:
(-6 + x)(6 + x)(-36 + x2) = 0

Multiply (-6 + x) * (6 + x)
(-6(6 + x) + x(6 + x))(-36 + x2) = 0
((6 * -6 + x * -6) + x(6 + x))(-36 + x2) = 0
((-36 + -6x) + x(6 + x))(-36 + x2) = 0
(-36 + -6x + (6 * x + x * x))(-36 + x2) = 0
(-36 + -6x + (6x + x2))(-36 + x2) = 0

Combine like terms: -6x + 6x = 0
(-36 + 0 + x2)(-36 + x2) = 0
(-36 + x2)(-36 + x2) = 0

Multiply (-36 + x2) * (-36 + x2)
(-36(-36 + x2) + x2(-36 + x2)) = 0
((-36 * -36 + x2 * -36) + x2(-36 + x2)) = 0
((1296 + -36x2) + x2(-36 + x2)) = 0
(1296 + -36x2 + (-36 * x2 + x2 * x2)) = 0
(1296 + -36x2 + (-36x2 + x4)) = 0

Combine like terms: -36x2 + -36x2 = -72x2
(1296 + -72x2 + x4) = 0

Solving
1296 + -72x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(36 + -1x2)(36 + -1x2) = 0

Factor a difference between two squares.
((6 + x)(6 + -1x))(36 + -1x2) = 0

Factor a difference between two squares.
((6 + x)(6 + -1x))(6 + x)(6 + -1x) = 0

Subproblem 1

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Subproblem 4

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

Solution

x = {-6, 6, -6, 6}

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