(x-3)(x+3)(x^2-11)=35

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Solution for (x-3)(x+3)(x^2-11)=35 equation:


Simplifying
(x + -3)(x + 3)(x2 + -11) = 35

Reorder the terms:
(-3 + x)(x + 3)(x2 + -11) = 35

Reorder the terms:
(-3 + x)(3 + x)(x2 + -11) = 35

Reorder the terms:
(-3 + x)(3 + x)(-11 + x2) = 35

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x))(-11 + x2) = 35
((3 * -3 + x * -3) + x(3 + x))(-11 + x2) = 35
((-9 + -3x) + x(3 + x))(-11 + x2) = 35
(-9 + -3x + (3 * x + x * x))(-11 + x2) = 35
(-9 + -3x + (3x + x2))(-11 + x2) = 35

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2)(-11 + x2) = 35
(-9 + x2)(-11 + x2) = 35

Multiply (-9 + x2) * (-11 + x2)
(-9(-11 + x2) + x2(-11 + x2)) = 35
((-11 * -9 + x2 * -9) + x2(-11 + x2)) = 35
((99 + -9x2) + x2(-11 + x2)) = 35
(99 + -9x2 + (-11 * x2 + x2 * x2)) = 35
(99 + -9x2 + (-11x2 + x4)) = 35

Combine like terms: -9x2 + -11x2 = -20x2
(99 + -20x2 + x4) = 35

Solving
99 + -20x2 + x4 = 35

Solving for variable 'x'.

Reorder the terms:
99 + -35 + -20x2 + x4 = 35 + -35

Combine like terms: 99 + -35 = 64
64 + -20x2 + x4 = 35 + -35

Combine like terms: 35 + -35 = 0
64 + -20x2 + x4 = 0

Factor a trinomial.
(4 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(16 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(2 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 3

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 4

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-2, 2, -4, 4}

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