35x^2=31x-6

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

Simplifying
35x2 = 31x + -6

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

Solving
35x2 = -6 + 31x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(2 + -7x)(3 + -5x) = 0

Subproblem 1
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0.2857142857, 0.6}