14x+105=7x^2

Solution for 14x+105=7x^2 equation:

Simplifying
14x + 105 = 7x2

Reorder the terms:
105 + 14x = 7x2

Solving
105 + 14x = 7x2

Solving for variable 'x'.

Combine like terms: 7x2 + -7x2 = 0
105 + 14x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(15 + 2x + -1x2) = 0

Factor a trinomial.
7((5 + -1x)(3 + x)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {5, -3}