In Exercises 101–106, solve each equation.$x(x+1{)}^3-42(x+1{)}^2=0$

In Exercises 101–106, solve each equation. $\mid x^2+2x-36\mid =12$

In Exercises 91–100, find all values of x satisfying the given conditions.$y_1 = 6 \(\left\)( \(\frac{2x}{x - 3}\) \(\right\))^2, \(\quad\) y_2 = 5 \(\left\)( \(\frac{2x}{x - 3}\) \(\right\)), \(\quad\) \(\text{and}\) \(\quad\) y_1 \(\text{ exceeds }\) y_2 \(\text{ by }\) 6.$

In Exercises 91–100, find all values of x satisfying the given conditions. $y = x - \(\sqrt{x - 2}\) \(\quad\) \(\text{and}\) \(\quad\) y = 4$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(2x + 3) + √(x - 2) = 2

Solve each equation in Exercises 41–60 by making an appropriate substitution. $9x^4=25x^2-16$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $3x^4=81x$

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | 3x² - 14x | = 5