e(12x+7)+e(6x^2+7x+1)=0

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Solution for e(12x+7)+e(6x^2+7x+1)=0 equation: 


Simplifying
e(12x + 7) + e(6x2 + 7x + 1) = 0

Reorder the terms:
e(7 + 12x) + e(6x2 + 7x + 1) = 0
(7 * e + 12x * e) + e(6x2 + 7x + 1) = 0
(7e + 12ex) + e(6x2 + 7x + 1) = 0

Reorder the terms:
7e + 12ex + e(1 + 7x + 6x2) = 0
7e + 12ex + (1 * e + 7x * e + 6x2 * e) = 0
7e + 12ex + (1e + 7ex + 6ex2) = 0

Reorder the terms:
7e + 1e + 12ex + 7ex + 6ex2 = 0

Combine like terms: 7e + 1e = 8e
8e + 12ex + 7ex + 6ex2 = 0

Combine like terms: 12ex + 7ex = 19ex
8e + 19ex + 6ex2 = 0

Solving
8e + 19ex + 6ex2 = 0

Solving for variable 'e'.

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

Factor out the Greatest Common Factor (GCF), 'e'.
e(8 + 19x + 6x2) = 0

Factor a trinomial.
e((8 + 3x)(1 + 2x)) = 0


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

Simplifying
e = 0

Solving
e = 0

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

Simplifying
e = 0

Subproblem 2
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Add '-3x' to each side of the equation.
3x + -3x = -8 + -3x

Combine like terms: 3x + -3x = 0
0 = -8 + -3x

Simplifying
0 = -8 + -3x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Add '-2x' to each side of the equation.
2x + -2x = -1 + -2x

Combine like terms: 2x + -2x = 0
0 = -1 + -2x

Simplifying
0 = -1 + -2x

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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