What is the general solution for 12sin^2(x)-20sin(x)=-8 ?

The general solution for 12sin^2(x)-20sin(x)=-8 is x= pi/2+2pin,x=0.72972…+2pin,x=pi-0.72972…+2pin

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12sin^2(x)-20sin(x)=-8

12 sin^{2} (x) - 20 sin (x) = - 8

x = \frac{π}{2} + 2 πn, x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

Solution steps

12 sin^{2} (x) - 20 sin (x) = - 8

Solve by substitution

sin (x) = 1, sin (x) = \frac{2}{3}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{2}{3} : x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

6 arccos (4 x) = π

- 4 sin (x) cos (x) = 2 sin (x)

7 sin^{2} (θ) + 16 sin (θ) + 9 = 0

3 tan (\frac{3 π}{4} (x + \frac{3 π}{2})) = 1

tan (x) = \frac{10}{4}

What is the general solution for 12sin^2(x)-20sin(x)=-8 ?
The general solution for 12sin^2(x)-20sin(x)=-8 is x= pi/2+2pin,x=0.72972…+2pin,x=pi-0.72972…+2pin