35e^2=3(2e+3)

Solution for 35e^2=3(2e+3) equation:

Simplifying
35e2 = 3(2e + 3)

Reorder the terms:
35e2 = 3(3 + 2e)
35e2 = (3 * 3 + 2e * 3)
35e2 = (9 + 6e)

Solving
35e2 = 9 + 6e

Solving for variable 'e'.

Reorder the terms:
-9 + -6e + 35e2 = 9 + 6e + -9 + -6e

Reorder the terms:
-9 + -6e + 35e2 = 9 + -9 + 6e + -6e

Combine like terms: 9 + -9 = 0
-9 + -6e + 35e2 = 0 + 6e + -6e
-9 + -6e + 35e2 = 6e + -6e

Combine like terms: 6e + -6e = 0
-9 + -6e + 35e2 = 0

Factor a trinomial.
(-3 + -7e)(3 + -5e) = 0

Subproblem 1
Set the factor '(-3 + -7e)' equal to zero and attempt to solve:

Simplifying
-3 + -7e = 0

Solving
-3 + -7e = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7e = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7e = 0 + 3
-7e = 0 + 3

Combine like terms: 0 + 3 = 3
-7e = 3

Divide each side by '-7'.
e = -0.4285714286

Simplifying
e = -0.4285714286
Subproblem 2
Set the factor '(3 + -5e)' equal to zero and attempt to solve:

Simplifying
3 + -5e = 0

Solving
3 + -5e = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5e = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5e = 0 + -3
-5e = 0 + -3

Combine like terms: 0 + -3 = -3
-5e = -3

Divide each side by '-5'.
e = 0.6

Simplifying
e = 0.6
Solution
e = {-0.4285714286, 0.6}