4=16sin(a)(1.6sin(a))-5*1.6sin(a)*1.6sin(a)

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Solution for 4=16sin(a)(1.6sin(a))-5*1.6sin(a)*1.6sin(a) equation: 


Simplifying
4 = 16sin(a)(1.6sin(a)) + -5 * 1.6sin(a) * 1.6sin(a)

Multiply ins * a
4 = 16ins * a(1.6ains) + -5 * 1.6sin(a) * 1.6sin(a)

Remove parenthesis around (1.6ains)
4 = 16ins * a * 1.6ains + -5 * 1.6sin(a) * 1.6sin(a)

Reorder the terms for easier multiplication:
4 = 16 * 1.6ins * a * ains + -5 * 1.6sin(a) * 1.6sin(a)

Multiply 16 * 1.6
4 = 25.6ins * a * ains + -5 * 1.6sin(a) * 1.6sin(a)

Multiply ins * a
4 = 25.6ains * ains + -5 * 1.6sin(a) * 1.6sin(a)

Multiply ains * ains
4 = 25.6a2i2n2s2 + -5 * 1.6sin(a) * 1.6sin(a)

Reorder the terms for easier multiplication:
4 = 25.6a2i2n2s2 + -5 * 1.6 * 1.6ins * a * ins * a

Multiply -5 * 1.6
4 = 25.6a2i2n2s2 + -8 * 1.6ins * a * ins * a

Multiply -8 * 1.6
4 = 25.6a2i2n2s2 + -12.8ins * a * ins * a

Multiply ins * a
4 = 25.6a2i2n2s2 + -12.8ains * ins * a

Multiply ains * ins
4 = 25.6a2i2n2s2 + -12.8ai2n2s2 * a

Multiply ai2n2s2 * a
4 = 25.6a2i2n2s2 + -12.8a2i2n2s2

Combine like terms: 25.6a2i2n2s2 + -12.8a2i2n2s2 = 12.8a2i2n2s2
4 = 12.8a2i2n2s2

Solving
4 = 12.8a2i2n2s2

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-12.8a2i2n2s2' to each side of the equation.
4 + -12.8a2i2n2s2 = 12.8a2i2n2s2 + -12.8a2i2n2s2

Combine like terms: 12.8a2i2n2s2 + -12.8a2i2n2s2 = 0.0
4 + -12.8a2i2n2s2 = 0.0

Add '-4' to each side of the equation.
4 + -4 + -12.8a2i2n2s2 = 0.0 + -4

Combine like terms: 4 + -4 = 0
0 + -12.8a2i2n2s2 = 0.0 + -4
-12.8a2i2n2s2 = 0.0 + -4

Combine like terms: 0.0 + -4 = -4
-12.8a2i2n2s2 = -4

Divide each side by '-12.8i2n2s2'.
a2 = 0.3125i-2n-2s-2

Simplifying
a2 = 0.3125i-2n-2s-2

Take the square root of each side:
a = {-0.559016994i-1n-1s-1, 0.559016994i-1n-1s-1}

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