Solve 6a-3(t-5)=2(t-5)

$$6 a - 3 ( t - 5 ) = 2 ( t - 5 )$$

Solve for a

$$a=\frac{5\left(t-5\right)}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by t-5.

$$6a-3t+15=2\left(t-5\right)$$

Use the distributive property to multiply 2 by t-5.

$$6a-3t+15=2t-10$$

Add 3t to both sides.

$$6a+15=2t-10+3t$$

Combine 2t and 3t to get 5t.

$$6a+15=5t-10$$

Subtract 15 from both sides.

$$6a=5t-10-15$$

Subtract 15 from -10 to get -25.

$$6a=5t-25$$

Divide both sides by 6.

$$\frac{6a}{6}=\frac{5t-25}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$a=\frac{5t-25}{6}$$

Solve for t

$$t=\frac{6a}{5}+5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by t-5.

$$6a-3t+15=2\left(t-5\right)$$

Use the distributive property to multiply 2 by t-5.

$$6a-3t+15=2t-10$$

Subtract 2t from both sides.

$$6a-3t+15-2t=-10$$

Combine -3t and -2t to get -5t.

$$6a-5t+15=-10$$

Subtract 6a from both sides.

$$-5t+15=-10-6a$$

Subtract 15 from both sides.

$$-5t=-10-6a-15$$

Subtract 15 from -10 to get -25.

$$-5t=-25-6a$$

The equation is in standard form.

$$-5t=-6a-25$$

Divide both sides by -5.

$$\frac{-5t}{-5}=\frac{-6a-25}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$t=\frac{-6a-25}{-5}$$

Divide -25-6a by -5.

$$t=\frac{6a}{5}+5$$