8x^2+6=x^2-23x

Solution for 8x^2+6=x^2-23x equation:

Simplifying
8x2 + 6 = x2 + -23x

Reorder the terms:
6 + 8x2 = x2 + -23x

Reorder the terms:
6 + 8x2 = -23x + x2

Solving
6 + 8x2 = -23x + x2

Solving for variable 'x'.

Reorder the terms:
6 + 23x + 8x2 + -1x2 = -23x + x2 + 23x + -1x2

Combine like terms: 8x2 + -1x2 = 7x2
6 + 23x + 7x2 = -23x + x2 + 23x + -1x2

Reorder the terms:
6 + 23x + 7x2 = -23x + 23x + x2 + -1x2

Combine like terms: -23x + 23x = 0
6 + 23x + 7x2 = 0 + x2 + -1x2
6 + 23x + 7x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 23x + 7x2 = 0

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

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Subproblem 2
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
Solution
x = {-3, -0.2857142857}