x(x+2)(x-2)-(x+5)(x^2-1)-3(x-1)=0

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Solution for x(x+2)(x-2)-(x+5)(x^2-1)-3(x-1)=0 equation:


Simplifying
x(x + 2)(x + -2) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0

Reorder the terms:
x(2 + x)(x + -2) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0

Reorder the terms:
x(2 + x)(-2 + x) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0

Multiply (2 + x) * (-2 + x)
x(2(-2 + x) + x(-2 + x)) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0
x((-2 * 2 + x * 2) + x(-2 + x)) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0
x((-4 + 2x) + x(-2 + x)) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0
x(-4 + 2x + (-2 * x + x * x)) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0
x(-4 + 2x + (-2x + x2)) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0

Combine like terms: 2x + -2x = 0
x(-4 + 0 + x2) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0
x(-4 + x2) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0
(-4 * x + x2 * x) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0
(-4x + x3) + -1(x + 5)(x2 + -1) + -3(x + -1) = 0

Reorder the terms:
-4x + x3 + -1(5 + x)(x2 + -1) + -3(x + -1) = 0

Reorder the terms:
-4x + x3 + -1(5 + x)(-1 + x2) + -3(x + -1) = 0

Multiply (5 + x) * (-1 + x2)
-4x + x3 + -1(5(-1 + x2) + x(-1 + x2)) + -3(x + -1) = 0
-4x + x3 + -1((-1 * 5 + x2 * 5) + x(-1 + x2)) + -3(x + -1) = 0
-4x + x3 + -1((-5 + 5x2) + x(-1 + x2)) + -3(x + -1) = 0
-4x + x3 + -1(-5 + 5x2 + (-1 * x + x2 * x)) + -3(x + -1) = 0
-4x + x3 + -1(-5 + 5x2 + (-1x + x3)) + -3(x + -1) = 0

Reorder the terms:
-4x + x3 + -1(-5 + -1x + 5x2 + x3) + -3(x + -1) = 0
-4x + x3 + -1(-5 + -1x + 5x2 + x3) + -3(x + -1) = 0
-4x + x3 + (-5 * -1 + -1x * -1 + 5x2 * -1 + x3 * -1) + -3(x + -1) = 0
-4x + x3 + (5 + 1x + -5x2 + -1x3) + -3(x + -1) = 0

Reorder the terms:
-4x + x3 + 5 + 1x + -5x2 + -1x3 + -3(-1 + x) = 0
-4x + x3 + 5 + 1x + -5x2 + -1x3 + (-1 * -3 + x * -3) = 0
-4x + x3 + 5 + 1x + -5x2 + -1x3 + (3 + -3x) = 0

Reorder the terms:
5 + 3 + -4x + 1x + -3x + -5x2 + x3 + -1x3 = 0

Combine like terms: 5 + 3 = 8
8 + -4x + 1x + -3x + -5x2 + x3 + -1x3 = 0

Combine like terms: -4x + 1x = -3x
8 + -3x + -3x + -5x2 + x3 + -1x3 = 0

Combine like terms: -3x + -3x = -6x
8 + -6x + -5x2 + x3 + -1x3 = 0

Combine like terms: x3 + -1x3 = 0
8 + -6x + -5x2 + 0 = 0
8 + -6x + -5x2 = 0

Solving
8 + -6x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -5x)(2 + x) = 0

Subproblem 1

Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 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 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8

Subproblem 2

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

Solution

x = {0.8, -2}

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