Complete the square
t^2+10t=75

COMPLETING THE SQUARE (PROCESS):
Do a reverse factoring procedure to develop the following form of equation:
(t + a)^2 = b

where:
t = unknown variable
a = coefficient
b = coefficient

Then take square root of both sides to find value of unknown variable as follows:

t^2 + 10t = 75
(t^2 + 10t + 25) = 75 + 25
(t^2 + 5t + 5t + 25) = 100
(t + 5)(t + 5) = 100
(t + 5)^2 = 100
√(t + 5)^2 = √100

Two solutions exist:
+(t + 5) = 10
AND
-(t + 5) = 10

Thus:
t = 10 - 5 = 5
AND
t = -5 - 10 = -15

$$t^2+10t=75 \\ t^2+10t+25-25=75\\ (t+5)^2=100\\ |t+5|=10\\ t+5=10 \vee t+5=-10\\ t=5 \vee t=-15$$