3e^2(2x+1)=2e^2-e^2(x+1)

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Solution for 3e^2(2x+1)=2e^2-e^2(x+1) equation:


Simplifying
3e2(2x + 1) = 2e2 + -1e2(x + 1)

Reorder the terms:
3e2(1 + 2x) = 2e2 + -1e2(x + 1)
(1 * 3e2 + 2x * 3e2) = 2e2 + -1e2(x + 1)
(3e2 + 6e2x) = 2e2 + -1e2(x + 1)

Reorder the terms:
3e2 + 6e2x = 2e2 + -1e2(1 + x)
3e2 + 6e2x = 2e2 + (1 * -1e2 + x * -1e2)
3e2 + 6e2x = 2e2 + (-1e2 + -1e2x)

Combine like terms: 2e2 + -1e2 = 1e2
3e2 + 6e2x = 1e2 + -1e2x

Solving
3e2 + 6e2x = 1e2 + -1e2x

Solving for variable 'e'.

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

Add '-1e2' to each side of the equation.
3e2 + -1e2 + 6e2x = 1e2 + -1e2 + -1e2x

Combine like terms: 3e2 + -1e2 = 2e2
2e2 + 6e2x = 1e2 + -1e2 + -1e2x

Combine like terms: 1e2 + -1e2 = 0
2e2 + 6e2x = 0 + -1e2x
2e2 + 6e2x = -1e2x

Add 'e2x' to each side of the equation.
2e2 + 6e2x + e2x = -1e2x + e2x

Combine like terms: 6e2x + e2x = 7e2x
2e2 + 7e2x = -1e2x + e2x

Combine like terms: -1e2x + e2x = 0
2e2 + 7e2x = 0

Factor out the Greatest Common Factor (GCF), 'e2'.
e2(2 + 7x) = 0


Subproblem 1
Set the factor 'e2' equal to zero and attempt to solve:

Simplifying
e2 = 0

Solving
e2 = 0

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

Simplifying
e2 = 0

Take the square root of each side:
e = {0}

Subproblem 2
Set the factor '(2 + 7x)' equal to zero and attempt to solve:

Simplifying
2 + 7x = 0

Solving
2 + 7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x = 0 + -2
7x = 0 + -2

Combine like terms: 0 + -2 = -2
7x = -2

Add '-7x' to each side of the equation.
7x + -7x = -2 + -7x

Combine like terms: 7x + -7x = 0
0 = -2 + -7x

Simplifying
0 = -2 + -7x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
e = {0}

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