[(8x^5)+(10x^4)]-[(4x^3)-(5x)]=0
To solve the equation [(8x^5) + (10x^4)] - [(4x^3) - (5x)] = 0, we need to simplify the expression and find the values of x that make it equal to zero.
Step 1: Simplify the expression by distributing the negative sign in front of the second set of brackets:
(8x^5) + (10x^4) - 4x^3 + 5x = 0
Step 2: Combine like terms:
8x^5 + 10x^4 - 4x^3 + 5x = 0
Step 3: Rearrange the terms to make it easier to factor:
8x^5 + 10x^4 - 4x^3 + 5x - 0 = 0
Step 4: Factor out the common factor, if possible:
x(8x^4 + 10x^3 - 4x^2 + 5) = 0
Step 5: Set each factor equal to zero and solve for x:
Case 1: x = 0
Case 2: 8x^4 + 10x^3 - 4x^2 + 5 = 0
At this point, we can either attempt to factor the quartic equation or use numerical methods such as graphing or using a calculator to find the approximate solutions.
If you choose to factor, as the equation is quite complex, you can use other mathematical software or calculators to factor the equation if it is factorable or proceed with numerical methods to approximate the solutions.