Find the solutions/ show steps
Sin2x+sin(4x) =0

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

Step-by-step explanation:

sin(2x) + sin(4x) = 0

Use double angle formula.

sin(2x) + 2 sin(2x) cos(2x) = 0

Factor.

sin(2x) (1 + 2 cos(2x)) = 0

Solve.

sin(2x) = 0, cos(2x) = -½

2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

answer: sorry

step-by-step explanation: can you tell me pls how to find the rational of two integers