solve(3D^2+D-14)y=13e^2x

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Solution for solve(3D^2+D-14)y=13e^2x equation: 


Simplifying
solve(3D2 + D + -14) * y = 13e2x

Reorder the terms:
elosv(-14 + D + 3D2) * y = 13e2x

Reorder the terms for easier multiplication:
elosv * y(-14 + D + 3D2) = 13e2x

Multiply elosv * y
elosvy(-14 + D + 3D2) = 13e2x
(-14 * elosvy + D * elosvy + 3D2 * elosvy) = 13e2x
(-14elosvy + elosvyD + 3elosvyD2) = 13e2x

Solving
-14elosvy + elosvyD + 3elosvyD2 = 13e2x

Solving for variable 'e'.

Combine like terms: 13e2x + -13e2x = 0
-14elosvy + elosvyD + 3elosvyD2 + -13e2x = 0

Factor out the Greatest Common Factor (GCF), 'e'.
e(-14losvy + losvyD + 3losvyD2 + -13ex) = 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 '(-14losvy + losvyD + 3losvyD2 + -13ex)' equal to zero and attempt to solve:

Simplifying
-14losvy + losvyD + 3losvyD2 + -13ex = 0

Reorder the terms:
-13ex + -14losvy + losvyD + 3losvyD2 = 0

Solving
-13ex + -14losvy + losvyD + 3losvyD2 = 0

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

Add '14losvy' to each side of the equation.
-13ex + -14losvy + losvyD + 14losvy + 3losvyD2 = 0 + 14losvy

Reorder the terms:
-13ex + -14losvy + 14losvy + losvyD + 3losvyD2 = 0 + 14losvy

Combine like terms: -14losvy + 14losvy = 0
-13ex + 0 + losvyD + 3losvyD2 = 0 + 14losvy
-13ex + losvyD + 3losvyD2 = 0 + 14losvy
Remove the zero:
-13ex + losvyD + 3losvyD2 = 14losvy

Add '-1losvyD' to each side of the equation.
-13ex + losvyD + -1losvyD + 3losvyD2 = 14losvy + -1losvyD

Combine like terms: losvyD + -1losvyD = 0
-13ex + 0 + 3losvyD2 = 14losvy + -1losvyD
-13ex + 3losvyD2 = 14losvy + -1losvyD

Add '-3losvyD2' to each side of the equation.
-13ex + 3losvyD2 + -3losvyD2 = 14losvy + -1losvyD + -3losvyD2

Combine like terms: 3losvyD2 + -3losvyD2 = 0
-13ex + 0 = 14losvy + -1losvyD + -3losvyD2
-13ex = 14losvy + -1losvyD + -3losvyD2

Divide each side by '-13x'.
e = -1.076923077losvx-1y + 0.07692307692losvx-1yD + 0.2307692308losvx-1yD2

Simplifying
e = -1.076923077losvx-1y + 0.07692307692losvx-1yD + 0.2307692308losvx-1yD2
Solution
e = {0, -1.076923077losvx-1y + 0.07692307692losvx-1yD + 0.2307692308losvx-1yD2}

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