Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$t=\dfrac{106}{27}$
Raising both sides to the fourth power results to \begin{array}{l}\require{cancel} 3(4-t)^{1/4}=6^{1/4} \\\\ \left( 3(4-t)^{1/4} \right)^4=\left( 6^{1/4} \right)^4 \\\\ 81(4-t)=6 .\end{array} Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 81(4-t)=6 \\\\ 81(4)+81(-t)=6 \\\\ 324-81t=6 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 324-81t=6 \\\\ -81t=6-324 \\\\ -81t=-318 \\\\ t=\dfrac{-318}{-81} \\\\ t=\dfrac{106}{27} .\end{array} Upon checking, $t=\dfrac{106}{27}$ satisfies the original equation.