(x-3)(x+4)(x+3)(x-4)=0

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Solution for (x-3)(x+4)(x+3)(x-4)=0 equation:


Simplifying
(x + -3)(x + 4)(x + 3)(x + -4) = 0

Reorder the terms:
(-3 + x)(x + 4)(x + 3)(x + -4) = 0

Reorder the terms:
(-3 + x)(4 + x)(x + 3)(x + -4) = 0

Reorder the terms:
(-3 + x)(4 + x)(3 + x)(x + -4) = 0

Reorder the terms:
(-3 + x)(4 + x)(3 + x)(-4 + x) = 0

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x))(3 + x)(-4 + x) = 0
((4 * -3 + x * -3) + x(4 + x))(3 + x)(-4 + x) = 0
((-12 + -3x) + x(4 + x))(3 + x)(-4 + x) = 0
(-12 + -3x + (4 * x + x * x))(3 + x)(-4 + x) = 0
(-12 + -3x + (4x + x2))(3 + x)(-4 + x) = 0

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2)(3 + x)(-4 + x) = 0

Multiply (-12 + 1x + x2) * (3 + x)
(-12(3 + x) + 1x * (3 + x) + x2(3 + x))(-4 + x) = 0
((3 * -12 + x * -12) + 1x * (3 + x) + x2(3 + x))(-4 + x) = 0
((-36 + -12x) + 1x * (3 + x) + x2(3 + x))(-4 + x) = 0
(-36 + -12x + (3 * 1x + x * 1x) + x2(3 + x))(-4 + x) = 0
(-36 + -12x + (3x + 1x2) + x2(3 + x))(-4 + x) = 0
(-36 + -12x + 3x + 1x2 + (3 * x2 + x * x2))(-4 + x) = 0
(-36 + -12x + 3x + 1x2 + (3x2 + x3))(-4 + x) = 0

Combine like terms: -12x + 3x = -9x
(-36 + -9x + 1x2 + 3x2 + x3)(-4 + x) = 0

Combine like terms: 1x2 + 3x2 = 4x2
(-36 + -9x + 4x2 + x3)(-4 + x) = 0

Multiply (-36 + -9x + 4x2 + x3) * (-4 + x)
(-36(-4 + x) + -9x * (-4 + x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0
((-4 * -36 + x * -36) + -9x * (-4 + x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0
((144 + -36x) + -9x * (-4 + x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0
(144 + -36x + (-4 * -9x + x * -9x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0
(144 + -36x + (36x + -9x2) + 4x2 * (-4 + x) + x3(-4 + x)) = 0
(144 + -36x + 36x + -9x2 + (-4 * 4x2 + x * 4x2) + x3(-4 + x)) = 0
(144 + -36x + 36x + -9x2 + (-16x2 + 4x3) + x3(-4 + x)) = 0
(144 + -36x + 36x + -9x2 + -16x2 + 4x3 + (-4 * x3 + x * x3)) = 0
(144 + -36x + 36x + -9x2 + -16x2 + 4x3 + (-4x3 + x4)) = 0

Combine like terms: -36x + 36x = 0
(144 + 0 + -9x2 + -16x2 + 4x3 + -4x3 + x4) = 0
(144 + -9x2 + -16x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: -9x2 + -16x2 = -25x2
(144 + -25x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: 4x3 + -4x3 = 0
(144 + -25x2 + 0 + x4) = 0
(144 + -25x2 + x4) = 0

Solving
144 + -25x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(16 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(3 + x)(3 + -1x) = 0

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

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 = {-3, 3, -4, 4}

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