Question 1177908
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One solution by inspection is x=0.  Other solutions, if any, can probably only be obtained approximately using calculus or a graphing calculator.<br>
If you want help with this, re-post your question, making sure you have posted the equation correctly.  As posted, the equation is this:<br>
{{{2(2^x- 1) x^2 + (2^(x^2)-2)x = 2^(x+1) -2}}}<br>
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If that was indeed the correct equation, then what I said in my original response is correct: there is no algebraic method for solving the equation; numerical methods using calculus or a graphing calculator are required.<br>