(12x-1)(3x%2B2)(x%2B1)-4%3D0.jpeg "(4x+1)(12x-1)(3x+2)(x+1)-4=0")
Solving the Equation: (4x+1)(12x-1)(3x+2)(x+1)-4=0
In this article, we will solve the equation:
$(4x+1)(12x-1)(3x+2)(x+1)-4=0$
Expanding the Equation
To solve this equation, we need to expand the product of the four binomials. Using the distributive property of multiplication over addition, we get:
$(4x+1)(12x-1)(3x+2)(x+1)-4=0$
$=(48x^2+12x-4x-1)(3x+2)(x+1)-4=0$
$=(48x^2+8x-1)(3x+2)(x+1)-4=0$
$=(144x^3+24x^2-3x-2)(x+1)-4=0$
$=144x^4+168x^3+21x^2-7x-2-4=0$
Simplifying the Equation
Now, we can simplify the equation by combining like terms:
$144x^4+168x^3+21x^2-7x-6=0$
Finding the Roots
To solve for x, we need to find the roots of the equation. Unfortunately, this equation is a quartic equation, which is not easily solvable using elementary algebra. However, we can use numerical methods or computer algebra systems to find the approximate roots of the equation.
Conclusion
In this article, we expanded and simplified the equation (4x+1)(12x-1)(3x+2)(x+1)-4=0. Unfortunately, solving for x involves finding the roots of a quartic equation, which is a challenging task. However, using numerical methods or computer algebra systems, we can approximate the roots of the equation.
