5x^2-6=-1x

Solution for 5x^2-6=-1x equation:

Simplifying
5x2 + -6 = -1x

Reorder the terms:
-6 + 5x2 = -1x

Solving
-6 + 5x2 = -1x

Solving for variable 'x'.

Reorder the terms:
-6 + x + 5x2 = -1x + x

Combine like terms: -1x + x = 0
-6 + x + 5x2 = 0

Factor a trinomial.
(-6 + -5x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 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 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.2, 1}