Solve 2(t+3)+3(t-4)=3(t-9)-7(6+t)

$$2 ( t + 3 ) + 3 ( t - 4 ) = 3 ( t - 9 ) - 7 ( 6 + t )$$

Solve for t

$$t=-7$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by t+3.

$$2t+6+3\left(t-4\right)=3\left(t-9\right)-7\left(6+t\right)$$

Use the distributive property to multiply 3 by t-4.

$$2t+6+3t-12=3\left(t-9\right)-7\left(6+t\right)$$

Combine 2t and 3t to get 5t.

$$5t+6-12=3\left(t-9\right)-7\left(6+t\right)$$

Subtract 12 from 6 to get -6.

$$5t-6=3\left(t-9\right)-7\left(6+t\right)$$

Use the distributive property to multiply 3 by t-9.

$$5t-6=3t-27-7\left(6+t\right)$$

Use the distributive property to multiply -7 by 6+t.

$$5t-6=3t-27-42-7t$$

Subtract 42 from -27 to get -69.

$$5t-6=3t-69-7t$$

Combine 3t and -7t to get -4t.

$$5t-6=-4t-69$$

Add 4t to both sides.

$$5t-6+4t=-69$$

Combine 5t and 4t to get 9t.

$$9t-6=-69$$

Add 6 to both sides.

$$9t=-69+6$$

Add -69 and 6 to get -63.

$$9t=-63$$

Divide both sides by 9.

$$t=\frac{-63}{9}$$

Divide -63 by 9 to get -7.

$$t=-7$$