(2x^2-5x-12)*(2cosx+1)=0

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Solution for (2x^2-5x-12)*(2cosx+1)=0 equation: 


Simplifying
(2x2 + -5x + -12)(2cosx + 1) = 0

Reorder the terms:
(-12 + -5x + 2x2)(2cosx + 1) = 0

Reorder the terms:
(-12 + -5x + 2x2)(1 + 2cosx) = 0

Multiply (-12 + -5x + 2x2) * (1 + 2cosx)
(-12(1 + 2cosx) + -5x * (1 + 2cosx) + 2x2 * (1 + 2cosx)) = 0
((1 * -12 + 2cosx * -12) + -5x * (1 + 2cosx) + 2x2 * (1 + 2cosx)) = 0
((-12 + -24cosx) + -5x * (1 + 2cosx) + 2x2 * (1 + 2cosx)) = 0
(-12 + -24cosx + (1 * -5x + 2cosx * -5x) + 2x2 * (1 + 2cosx)) = 0

Reorder the terms:
(-12 + -24cosx + (-10cosx2 + -5x) + 2x2 * (1 + 2cosx)) = 0
(-12 + -24cosx + (-10cosx2 + -5x) + 2x2 * (1 + 2cosx)) = 0
(-12 + -24cosx + -10cosx2 + -5x + (1 * 2x2 + 2cosx * 2x2)) = 0

Reorder the terms:
(-12 + -24cosx + -10cosx2 + -5x + (4cosx3 + 2x2)) = 0
(-12 + -24cosx + -10cosx2 + -5x + (4cosx3 + 2x2)) = 0

Reorder the terms:
(-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2) = 0
(-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2) = 0

Solving
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 0

Solving for variable 'c'.

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

Add '12' to each side of the equation.
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 12 + 2x2 = 0 + 12

Reorder the terms:
-12 + 12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 0 + 12
-24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 12

Add '5x' to each side of the equation.
-24cosx + -10cosx2 + 4cosx3 + -5x + 5x + 2x2 = 12 + 5x

Combine like terms: -5x + 5x = 0
-24cosx + -10cosx2 + 4cosx3 + 0 + 2x2 = 12 + 5x
-24cosx + -10cosx2 + 4cosx3 + 2x2 = 12 + 5x

Add '-2x2' to each side of the equation.
-24cosx + -10cosx2 + 4cosx3 + 2x2 + -2x2 = 12 + 5x + -2x2

Combine like terms: 2x2 + -2x2 = 0
-24cosx + -10cosx2 + 4cosx3 + 0 = 12 + 5x + -2x2
-24cosx + -10cosx2 + 4cosx3 = 12 + 5x + -2x2

Reorder the terms:
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 12 + 5x + -2x2 + -12 + -5x + 2x2

Reorder the terms:
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 12 + -12 + 5x + -5x + -2x2 + 2x2

Combine like terms: 12 + -12 = 0
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 0 + 5x + -5x + -2x2 + 2x2
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 5x + -5x + -2x2 + 2x2

Combine like terms: 5x + -5x = 0
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 0 + -2x2 + 2x2
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-12 + -24cosx + -10cosx2 + 4cosx3 + -5x + 2x2 = 0

The solution to this equation could not be determined.

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