Solve 4t(t-5)-2t(3t+2)+108=3t(2t-5)-t(8t-3)

$$4 t ( t - 5 ) - 2 t ( 3 t + 2 ) + 108 = 3 t ( 2 t - 5 ) - t ( 8 t - 3 )$$

Solve for t

$$t=9$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4t by t-5.

$$4t^{2}-20t-2t\left(3t+2\right)+108=3t\left(2t-5\right)-t\left(8t-3\right)$$

Use the distributive property to multiply 3t by 2t-5.

$$4t^{2}-20t-2t\left(3t+2\right)+108=6t^{2}-15t-t\left(8t-3\right)$$

Use the distributive property to multiply t by 8t-3.

$$4t^{2}-20t-2t\left(3t+2\right)+108=6t^{2}-15t-\left(8t^{2}-3t\right)$$

To find the opposite of 8t^{2}-3t, find the opposite of each term.

$$4t^{2}-20t-2t\left(3t+2\right)+108=6t^{2}-15t-8t^{2}-\left(-3t\right)$$

The opposite of -3t is 3t.

$$4t^{2}-20t-2t\left(3t+2\right)+108=6t^{2}-15t-8t^{2}+3t$$

Combine 6t^{2} and -8t^{2} to get -2t^{2}.

$$4t^{2}-20t-2t\left(3t+2\right)+108=-2t^{2}-15t+3t$$

Combine -15t and 3t to get -12t.

$$4t^{2}-20t-2t\left(3t+2\right)+108=-2t^{2}-12t$$

Add 2t^{2} to both sides.

$$4t^{2}-20t-2t\left(3t+2\right)+108+2t^{2}=-12t$$

Add 12t to both sides.

$$4t^{2}-20t-2t\left(3t+2\right)+108+2t^{2}+12t=0$$

Subtract 108 from both sides. Anything subtracted from zero gives its negation.

$$4t^{2}-20t-2t\left(3t+2\right)+2t^{2}+12t=-108$$

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

$$4t^{2}-20t-6t^{2}-4t+2t^{2}+12t=-108$$

Combine 4t^{2} and -6t^{2} to get -2t^{2}.

$$-2t^{2}-20t-4t+2t^{2}+12t=-108$$

Combine -20t and -4t to get -24t.

$$-2t^{2}-24t+2t^{2}+12t=-108$$

Combine -2t^{2} and 2t^{2} to get 0.

$$-24t+12t=-108$$

Combine -24t and 12t to get -12t.

$$-12t=-108$$

Divide both sides by -12.

$$t=\frac{-108}{-12}$$

Divide -108 by -12 to get 9.

$$t=9$$