3x^2+120=4x^2+14x

Solution for 3x^2+120=4x^2+14x equation:

Simplifying
3x2 + 120 = 4x2 + 14x

Reorder the terms:
120 + 3x2 = 4x2 + 14x

Reorder the terms:
120 + 3x2 = 14x + 4x2

Solving
120 + 3x2 = 14x + 4x2

Solving for variable 'x'.

Reorder the terms:
120 + -14x + 3x2 + -4x2 = 14x + 4x2 + -14x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
120 + -14x + -1x2 = 14x + 4x2 + -14x + -4x2

Reorder the terms:
120 + -14x + -1x2 = 14x + -14x + 4x2 + -4x2

Combine like terms: 14x + -14x = 0
120 + -14x + -1x2 = 0 + 4x2 + -4x2
120 + -14x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
120 + -14x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(20 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 0

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

Add '-20' to each side of the equation.
20 + -20 + x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + x = 0 + -20
x = 0 + -20

Combine like terms: 0 + -20 = -20
x = -20

Simplifying
x = -20
Solution
x = {6, -20}