10(x^2+1)=13+x

Solution for 10(x^2+1)=13+x equation:

Simplifying
10(x2 + 1) = 13 + x

Reorder the terms:
10(1 + x2) = 13 + x
(1 * 10 + x2 * 10) = 13 + x
(10 + 10x2) = 13 + x

Solving
10 + 10x2 = 13 + x

Solving for variable 'x'.

Reorder the terms:
10 + -13 + -1x + 10x2 = 13 + x + -13 + -1x

Combine like terms: 10 + -13 = -3
-3 + -1x + 10x2 = 13 + x + -13 + -1x

Reorder the terms:
-3 + -1x + 10x2 = 13 + -13 + x + -1x

Combine like terms: 13 + -13 = 0
-3 + -1x + 10x2 = 0 + x + -1x
-3 + -1x + 10x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + -1x + 10x2 = 0

Factor a trinomial.
(-1 + -2x)(3 + -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 '(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 = {-0.5, 0.6}