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Resposta:
Let's solve these expressions step-by-step:
1) Simplify the left-hand side: \( 12x^6 - 9x + 6x \)
Simplify the right-hand side: \( 3x^3 \)
\[
12x^6 - 3x = 3x^3
\]
This equation implies \((12x^6 - 3x-3x^3 =0)\) which needs explicitly finding x,
2) Simplify the left-hand side: \( 3x - 5x + 4x^2 \)
Simplify the right-hand side: \( x^2 \)
On the left-hand side, combine \(3x\) and \(-5x\):
\[
(3x - 5x + 4x^2) = -2x + 4x^2
\]
So, the equation becomes:
\[
-2x + 4x^2 = x^2
\]
Rearranging terms:
\[
4x^2 - x^2 - 2x = 0
\]
\[
3x^2 - 2x = 0
\]
Factor out an \(x\):
\[
x(3x - 2) = 0
\]
Therefore, \(x = 0\) or \(3x - 2 = 0\):
Solve \(3x - 2 = 0\):
\[
3x = 2 \implies x = \frac{2}{3}
\]
3) Simplify the left-hand side: \(-6x^7g^3 + 12x^5 y^2 - 2x^2g \)
Simplify the right-hand side: \(2xy\)
The equation:
\(-6 x7 g 3+ 12 x 5 y ² - 2x²g =2xy \)
Simplifying each term if it equates to
(-6x^7g^3 + 12x^5y^2 - 2x^2g = 2xy) solve numerically by isolating either variable \(x\) or \(g\). Calculations or numerical methods still show dependency on g or y cases must to solve explicitly.
Still, you might need more reversible manipulation by variable isolation explicitly otherwise they remain as they appear until leading terms reduce.
Let me know if you need any more solution elaboration!