x+3=14x^2

Solution for x+3=14x^2 equation:

Simplifying
x + 3 = 14x2

Reorder the terms:
3 + x = 14x2

Solving
3 + x = 14x2

Solving for variable 'x'.

Combine like terms: 14x2 + -14x2 = 0
3 + x + -14x2 = 0

Factor a trinomial.
(1 + -2x)(3 + 7x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x 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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(3 + 7x)' equal to zero and attempt to solve:

Simplifying
3 + 7x = 0

Solving
3 + 7x = 0

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

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

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

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

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

Simplifying
x = -0.4285714286
Solution
x = {0.5, -0.4285714286}