7x+21=14x^2

Solution for 7x+21=14x^2 equation:

Simplifying
7x + 21 = 14x2

Reorder the terms:
21 + 7x = 14x2

Solving
21 + 7x = 14x2

Solving for variable 'x'.

Combine like terms: 14x2 + -14x2 = 0
21 + 7x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + x + -2x2) = 0

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

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {1.5, -1}