3x^2+114=4x^2+13x

Solution for 3x^2+114=4x^2+13x equation:

Simplifying
3x2 + 114 = 4x2 + 13x

Reorder the terms:
114 + 3x2 = 4x2 + 13x

Reorder the terms:
114 + 3x2 = 13x + 4x2

Solving
114 + 3x2 = 13x + 4x2

Solving for variable 'x'.

Reorder the terms:
114 + -13x + 3x2 + -4x2 = 13x + 4x2 + -13x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
114 + -13x + -1x2 = 13x + 4x2 + -13x + -4x2

Reorder the terms:
114 + -13x + -1x2 = 13x + -13x + 4x2 + -4x2

Combine like terms: 13x + -13x = 0
114 + -13x + -1x2 = 0 + 4x2 + -4x2
114 + -13x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
114 + -13x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(19 + 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 '(19 + x)' equal to zero and attempt to solve:

Simplifying
19 + x = 0

Solving
19 + x = 0

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

Add '-19' to each side of the equation.
19 + -19 + x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + x = 0 + -19
x = 0 + -19

Combine like terms: 0 + -19 = -19
x = -19

Simplifying
x = -19
Solution
x = {6, -19}