Final answer:
The equation presented is a cubic polynomial that does not equate anything and therefore cannot be solved without further information. Techniques such as the quadratic formula, completing the square, and expanding expressions are various methods used in algebra to solve or simplify equations.
Step-by-step explanation:
The equation 6x^3+8x^2-4x is a polynomial, specifically a cubic polynomial, which is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. This polynomial does not equal anything by itself; it is not set equal to zero or any other number. Therefore, this polynomial cannot be directly solved without additional information. However, it can be factored or simplified, if needed, based on the context of the problem.
In dealing with quadratic equations such as x² + 1.2 x 10^-2x - 6.0 × 10^-3 = 0, one can use the quadratic formula to solve for the values of 'x' that satisfy the equation. A quadratic equation is typically in the form ax² + bx + c = 0. The quadratic formula, which solves such equations, is given by x = (-b ± √(b² - 4ac)) / (2a).
Completing the square, expanding expressions, and balancing equations are different techniques used to manipulate and solve equations in various branches of mathematics, specifically algebra. For instance, completing the square is a method used to solve quadratic equations that can't be easily factored. Expanding expressions involves multiplying and combining like terms to simplify an expression, which is often an essential step before applying other algebraic techniques.