Solve 5(t^2-3t+2)=t(5t-2)

$$5 ( t ^ { 2 } - 3 t + 2 ) = t ( 5 t - 2 )$$

Solve for t

$$t=\frac{10}{13}\approx 0.769230769$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by t^{2}-3t+2.

$$5t^{2}-15t+10=t\left(5t-2\right)$$

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

$$5t^{2}-15t+10=5t^{2}-2t$$

Subtract 5t^{2} from both sides.

$$5t^{2}-15t+10-5t^{2}=-2t$$

Combine 5t^{2} and -5t^{2} to get 0.

$$-15t+10=-2t$$

Add 2t to both sides.

$$-15t+10+2t=0$$

Combine -15t and 2t to get -13t.

$$-13t+10=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-13t=-10$$

Divide both sides by -13.

$$t=\frac{-10}{-13}$$

Fraction \frac{-10}{-13} can be simplified to \frac{10}{13} by removing the negative sign from both the numerator and the denominator.

$$t=\frac{10}{13}$$