This document provides the step-by-step solution to solving the equation -3(t-5)-2(2t+1)=-8. It shows multiplying terms inside parentheses, combining like terms, moving constants to one side of the equation, and finally solving for t by dividing both sides by the coefficient of t. The solution is t=-3.

1. Synthesis
Find a polynomial for the shaded area of each figure.
(21t+8)(4t)-(3t-4)(2t)
Here is the problem can someone show me how to do this?
Solution
-3(t-5)-2(2t+1)=-8 Multiply -3 by each term inside the parentheses. (-3t+15)-2(2t+1)=-8 Multiply
-2 by each term inside the parentheses. (-3t+15)+(-4t-2)=-8 Remove the parentheses that are not
needed from the expression. -3t+15-4t-2=-8 Since -3t and -4t are like terms, subtract 4t from -3t
to get -7t. -7t+15-2=-8 Subtract 2 from 15 to get 13. -7t+13=-8 Since 13 does not contain the
variable to solve for, move it to the right-hand side of the equation by subtracting 13 from both
sides. -7t=-13-8 Subtract 8 from -13 to get -21. -7t=-21 Divide each term in the equation by -7. -
(7t)/(-7)=-(21)/(-7) Simplify the left-hand side of the equation by canceling the common terms.
t=-(21)/(-7) Simplify the right-hand side of the equation by simplifying each term.