10x^2=2-x

Solution for 10x^2=2-x equation:

Simplifying
10x2 = 2 + -1x

Solving
10x2 = 2 + -1x

Solving for variable 'x'.

Reorder the terms:
-2 + x + 10x2 = 2 + -1x + -2 + x

Reorder the terms:
-2 + x + 10x2 = 2 + -2 + -1x + x

Combine like terms: 2 + -2 = 0
-2 + x + 10x2 = 0 + -1x + x
-2 + x + 10x2 = -1x + x

Combine like terms: -1x + x = 0
-2 + x + 10x2 = 0

Factor a trinomial.
(-1 + -2x)(2 + -5x) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-0.5, 0.4}