3x^2+102=4x^2+11x

Solution for 3x^2+102=4x^2+11x equation:

Simplifying
3x2 + 102 = 4x2 + 11x

Reorder the terms:
102 + 3x2 = 4x2 + 11x

Reorder the terms:
102 + 3x2 = 11x + 4x2

Solving
102 + 3x2 = 11x + 4x2

Solving for variable 'x'.

Reorder the terms:
102 + -11x + 3x2 + -4x2 = 11x + 4x2 + -11x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
102 + -11x + -1x2 = 11x + 4x2 + -11x + -4x2

Reorder the terms:
102 + -11x + -1x2 = 11x + -11x + 4x2 + -4x2

Combine like terms: 11x + -11x = 0
102 + -11x + -1x2 = 0 + 4x2 + -4x2
102 + -11x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
102 + -11x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(17 + 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 '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Simplifying
x = -17
Solution
x = {6, -17}