3x^2(x^2-8)+6x+5=4x^4-6x(4x-1)+4

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Solution for 3x^2(x^2-8)+6x+5=4x^4-6x(4x-1)+4 equation:


Simplifying
3x2(x2 + -8) + 6x + 5 = 4x4 + -6x(4x + -1) + 4

Reorder the terms:
3x2(-8 + x2) + 6x + 5 = 4x4 + -6x(4x + -1) + 4
(-8 * 3x2 + x2 * 3x2) + 6x + 5 = 4x4 + -6x(4x + -1) + 4
(-24x2 + 3x4) + 6x + 5 = 4x4 + -6x(4x + -1) + 4

Reorder the terms:
5 + 6x + -24x2 + 3x4 = 4x4 + -6x(4x + -1) + 4

Reorder the terms:
5 + 6x + -24x2 + 3x4 = 4x4 + -6x(-1 + 4x) + 4
5 + 6x + -24x2 + 3x4 = 4x4 + (-1 * -6x + 4x * -6x) + 4
5 + 6x + -24x2 + 3x4 = 4x4 + (6x + -24x2) + 4

Reorder the terms:
5 + 6x + -24x2 + 3x4 = 4 + 6x + -24x2 + 4x4

Add '-6x' to each side of the equation.
5 + 6x + -24x2 + -6x + 3x4 = 4 + 6x + -24x2 + -6x + 4x4

Reorder the terms:
5 + 6x + -6x + -24x2 + 3x4 = 4 + 6x + -24x2 + -6x + 4x4

Combine like terms: 6x + -6x = 0
5 + 0 + -24x2 + 3x4 = 4 + 6x + -24x2 + -6x + 4x4
5 + -24x2 + 3x4 = 4 + 6x + -24x2 + -6x + 4x4

Reorder the terms:
5 + -24x2 + 3x4 = 4 + 6x + -6x + -24x2 + 4x4

Combine like terms: 6x + -6x = 0
5 + -24x2 + 3x4 = 4 + 0 + -24x2 + 4x4
5 + -24x2 + 3x4 = 4 + -24x2 + 4x4

Add '24x2' to each side of the equation.
5 + -24x2 + 24x2 + 3x4 = 4 + -24x2 + 24x2 + 4x4

Combine like terms: -24x2 + 24x2 = 0
5 + 0 + 3x4 = 4 + -24x2 + 24x2 + 4x4
5 + 3x4 = 4 + -24x2 + 24x2 + 4x4

Combine like terms: -24x2 + 24x2 = 0
5 + 3x4 = 4 + 0 + 4x4
5 + 3x4 = 4 + 4x4

Solving
5 + 3x4 = 4 + 4x4

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x4' to each side of the equation.
5 + 3x4 + -4x4 = 4 + 4x4 + -4x4

Combine like terms: 3x4 + -4x4 = -1x4
5 + -1x4 = 4 + 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
5 + -1x4 = 4 + 0
5 + -1x4 = 4

Add '-5' to each side of the equation.
5 + -5 + -1x4 = 4 + -5

Combine like terms: 5 + -5 = 0
0 + -1x4 = 4 + -5
-1x4 = 4 + -5

Combine like terms: 4 + -5 = -1
-1x4 = -1

Divide each side by '-1'.
x4 = 1

Simplifying
x4 = 1

Reorder the terms:
-1 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + x4 = 0

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

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

Subproblem 1

Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

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

Subproblem 3

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

Solution

x = {-1, 1}

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