7e^2+5e-4=4e^2-3e-4

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Solution for 7e^2+5e-4=4e^2-3e-4 equation:


Simplifying
7e2 + 5e + -4 = 4e2 + -3e + -4

Reorder the terms:
-4 + 5e + 7e2 = 4e2 + -3e + -4

Reorder the terms:
-4 + 5e + 7e2 = -4 + -3e + 4e2

Add '4' to each side of the equation.
-4 + 5e + 4 + 7e2 = -4 + -3e + 4 + 4e2

Reorder the terms:
-4 + 4 + 5e + 7e2 = -4 + -3e + 4 + 4e2

Combine like terms: -4 + 4 = 0
0 + 5e + 7e2 = -4 + -3e + 4 + 4e2
5e + 7e2 = -4 + -3e + 4 + 4e2

Reorder the terms:
5e + 7e2 = -4 + 4 + -3e + 4e2

Combine like terms: -4 + 4 = 0
5e + 7e2 = 0 + -3e + 4e2
5e + 7e2 = -3e + 4e2

Solving
5e + 7e2 = -3e + 4e2

Solving for variable 'e'.

Reorder the terms:
5e + 3e + 7e2 + -4e2 = -3e + 4e2 + 3e + -4e2

Combine like terms: 5e + 3e = 8e
8e + 7e2 + -4e2 = -3e + 4e2 + 3e + -4e2

Combine like terms: 7e2 + -4e2 = 3e2
8e + 3e2 = -3e + 4e2 + 3e + -4e2

Reorder the terms:
8e + 3e2 = -3e + 3e + 4e2 + -4e2

Combine like terms: -3e + 3e = 0
8e + 3e2 = 0 + 4e2 + -4e2
8e + 3e2 = 4e2 + -4e2

Combine like terms: 4e2 + -4e2 = 0
8e + 3e2 = 0

Factor out the Greatest Common Factor (GCF), 'e'.
e(8 + 3e) = 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 + 3e)' equal to zero and attempt to solve: Simplifying 8 + 3e = 0 Solving 8 + 3e = 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 + 3e = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3e = 0 + -8 3e = 0 + -8 Combine like terms: 0 + -8 = -8 3e = -8 Divide each side by '3'. e = -2.666666667 Simplifying e = -2.666666667

Solution

e = {0, -2.666666667}

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