(6a^3-5ac^2+12c)-(4c-3a^3-2ac^2) is equivalent to:

To simplify the given expression, we need to distribute the negative sign to each term in the second set of parentheses and then combine like terms.<br /><br />$(6a^{3}-5ac^{2}+12c)-(4c-3a^{3}-2ac^{2})$<br /><br />Distribute the negative sign:<br /><br />$(6a^{3}-5ac^{2}+12c)-4c+3a^{3}+2ac^{2}$<br /><br />Combine like terms:<br /><br />$6a^{3}+3a^{3}-5ac^{2}+2ac^{2}+12c-4c$<br /><br />Simplify:<br /><br />$9a^{3}-3ac^{2}+8c$<br /><br />Therefore, the simplified expression is $9a^{3}-3ac^{2}+8c$.