(3sinx+2)(2sinx-5)=0

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Solution for (3sinx+2)(2sinx-5)=0 equation:


Simplifying
(3sinx + 2)(2sinx + -5) = 0

Reorder the terms:
(2 + 3insx)(2sinx + -5) = 0

Reorder the terms:
(2 + 3insx)(-5 + 2insx) = 0

Multiply (2 + 3insx) * (-5 + 2insx)
(2(-5 + 2insx) + 3insx * (-5 + 2insx)) = 0
((-5 * 2 + 2insx * 2) + 3insx * (-5 + 2insx)) = 0
((-10 + 4insx) + 3insx * (-5 + 2insx)) = 0
(-10 + 4insx + (-5 * 3insx + 2insx * 3insx)) = 0
(-10 + 4insx + (-15insx + 6i2n2s2x2)) = 0

Combine like terms: 4insx + -15insx = -11insx
(-10 + -11insx + 6i2n2s2x2) = 0

Solving
-10 + -11insx + 6i2n2s2x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-2 + -3insx)(5 + -2insx) = 0

Subproblem 1

Set the factor '(-2 + -3insx)' equal to zero and attempt to solve: Simplifying -2 + -3insx = 0 Solving -2 + -3insx = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3insx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3insx = 0 + 2 -3insx = 0 + 2 Combine like terms: 0 + 2 = 2 -3insx = 2 Divide each side by '-3nsx'. i = -0.6666666667n-1s-1x-1 Simplifying i = -0.6666666667n-1s-1x-1

Subproblem 2

Set the factor '(5 + -2insx)' equal to zero and attempt to solve: Simplifying 5 + -2insx = 0 Solving 5 + -2insx = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2insx = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2insx = 0 + -5 -2insx = 0 + -5 Combine like terms: 0 + -5 = -5 -2insx = -5 Divide each side by '-2nsx'. i = 2.5n-1s-1x-1 Simplifying i = 2.5n-1s-1x-1

Solution

i = {-0.6666666667n-1s-1x-1, 2.5n-1s-1x-1}

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