(2x^2+x+1)(2x^2+x-4)=-4

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Solution for (2x^2+x+1)(2x^2+x-4)=-4 equation:


Simplifying
(2x2 + x + 1)(2x2 + x + -4) = -4

Reorder the terms:
(1 + x + 2x2)(2x2 + x + -4) = -4

Reorder the terms:
(1 + x + 2x2)(-4 + x + 2x2) = -4

Multiply (1 + x + 2x2) * (-4 + x + 2x2)
(1(-4 + x + 2x2) + x(-4 + x + 2x2) + 2x2 * (-4 + x + 2x2)) = -4
((-4 * 1 + x * 1 + 2x2 * 1) + x(-4 + x + 2x2) + 2x2 * (-4 + x + 2x2)) = -4
((-4 + 1x + 2x2) + x(-4 + x + 2x2) + 2x2 * (-4 + x + 2x2)) = -4
(-4 + 1x + 2x2 + (-4 * x + x * x + 2x2 * x) + 2x2 * (-4 + x + 2x2)) = -4
(-4 + 1x + 2x2 + (-4x + x2 + 2x3) + 2x2 * (-4 + x + 2x2)) = -4
(-4 + 1x + 2x2 + -4x + x2 + 2x3 + (-4 * 2x2 + x * 2x2 + 2x2 * 2x2)) = -4
(-4 + 1x + 2x2 + -4x + x2 + 2x3 + (-8x2 + 2x3 + 4x4)) = -4

Reorder the terms:
(-4 + 1x + -4x + 2x2 + x2 + -8x2 + 2x3 + 2x3 + 4x4) = -4

Combine like terms: 1x + -4x = -3x
(-4 + -3x + 2x2 + x2 + -8x2 + 2x3 + 2x3 + 4x4) = -4

Combine like terms: 2x2 + x2 = 3x2
(-4 + -3x + 3x2 + -8x2 + 2x3 + 2x3 + 4x4) = -4

Combine like terms: 3x2 + -8x2 = -5x2
(-4 + -3x + -5x2 + 2x3 + 2x3 + 4x4) = -4

Combine like terms: 2x3 + 2x3 = 4x3
(-4 + -3x + -5x2 + 4x3 + 4x4) = -4

Add '4' to each side of the equation.
-4 + -3x + -5x2 + 4x3 + 4 + 4x4 = -4 + 4

Reorder the terms:
-4 + 4 + -3x + -5x2 + 4x3 + 4x4 = -4 + 4

Combine like terms: -4 + 4 = 0
0 + -3x + -5x2 + 4x3 + 4x4 = -4 + 4
-3x + -5x2 + 4x3 + 4x4 = -4 + 4

Combine like terms: -4 + 4 = 0
-3x + -5x2 + 4x3 + 4x4 = 0

Solving
-3x + -5x2 + 4x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -5x + 4x2 + 4x3) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-3 + -5x + 4x2 + 4x3)' equal to zero and attempt to solve:

Simplifying
-3 + -5x + 4x2 + 4x3 = 0

Solving
-3 + -5x + 4x2 + 4x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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