6x^2+4x-14=35-31x

Solution for 6x^2+4x-14=35-31x equation:

Simplifying
6x2 + 4x + -14 = 35 + -31x

Reorder the terms:
-14 + 4x + 6x2 = 35 + -31x

Solving
-14 + 4x + 6x2 = 35 + -31x

Solving for variable 'x'.

Reorder the terms:
-14 + -35 + 4x + 31x + 6x2 = 35 + -31x + -35 + 31x

Combine like terms: -14 + -35 = -49
-49 + 4x + 31x + 6x2 = 35 + -31x + -35 + 31x

Combine like terms: 4x + 31x = 35x
-49 + 35x + 6x2 = 35 + -31x + -35 + 31x

Reorder the terms:
-49 + 35x + 6x2 = 35 + -35 + -31x + 31x

Combine like terms: 35 + -35 = 0
-49 + 35x + 6x2 = 0 + -31x + 31x
-49 + 35x + 6x2 = -31x + 31x

Combine like terms: -31x + 31x = 0
-49 + 35x + 6x2 = 0

Factor a trinomial.
(-7 + -1x)(7 + -6x) = 0

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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-7, 1.166666667}