What is the answer to solvefor x,be^{-2x}+3y+3x=0 ?

The answer to solvefor x,be^{-2x}+3y+3x=0 is x=(\W(-(2e^{2y}b)/3)-2y)/(2)

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solvefor x,be^{-2x}+3y+3x=0

solve for

x, b e^{- 2 x} + 3 y + 3 x = 0

x = \frac{W ( - \frac{2 e ^{2 y} b}{3} ) - 2 y}{2}

Solution steps

b e^{- 2 x} + 3 y + 3 x = 0

Prepare

b e^{- 2 x} + 3 y + 3 x = 0

for Lambert form:

b = (- 3 x - 3 y) e^{2 x}

Rewrite the equation with

2 x + 2 y = u

and

x = \frac{u - 2 y}{2}

b = (- 3 \frac{u - 2 y}{2} - 3 y) e^{2 \frac{u - 2 y}{2}}

Simplify

b = e^{u - 2 y} (- \frac{3 ( u - 2 y )}{2} - 3 y)

Rewrite

b = e^{u - 2 y} (- \frac{3 ( u - 2 y )}{2} - 3 y)

in Lambert form:

e^{u} u = - \frac{2 e ^{2 y} b}{3}

Solve

e^{u} u = - \frac{2 e ^{2 y} b}{3} : u = W (- \frac{2 e ^{2 y} b}{3})

u = W (- \frac{2 e ^{2 y} b}{3})

Substitute back

u = 2 x + 2 y,

solve for

x

Solve

2 x + 2 y = W (- \frac{2 e ^{2 y} b}{3}) : x = \frac{W ( - \frac{2 e ^{2 y} b}{3} ) - 2 y}{2}

x = \frac{W ( - \frac{2 e ^{2 y} b}{3} ) - 2 y}{2}

2 x^{4} \cdot e^{- 2 x} = 0

7 + 15 e^{1 - 3 x} = 37

4^{x + 3} = 8^{x - 2}

\frac{6 ^{2 n - 4}}{a ^{2 - n}} = 9^{x}

4^{x} + 2^{x} - 20 = 0

What is the answer to solvefor x,be^{-2x}+3y+3x=0 ?
The answer to solvefor x,be^{-2x}+3y+3x=0 is x=(\W(-(2e^{2y}b)/3)-2y)/(2)