What are the steps you follow while solving for variables in an equation?
From easy to difficult or tricky or exhausting, how do you solve for variables in an equation. Is there any algorithm or strategy to solve it. I am new to such level of maths, so asking as a intermediate. You may forward a link that helped you. Thanks in advance.
Here is a question (of such difficulty), you may solve, so that the post doesn't seems too subjective.
Determine all solutions of the equation in Real number, $(x^2 + 3x – 4)^3 + (2x^2 – 5x + 3)^3 = (3x^2 – 2x – 1)^3$
Consider $\;x^2+3x-4=a\;,\;2x^2-5x+3=b\;$ and observe that the given equation is $\;a^3+b^3=(a+b)^3\;.$
$$a^3+b^3=a^3+b^3+3ab(a+b)$$ $$\implies ab(a+b)=0$$
Can you take it from here?