2x-1=10-9x^2

Solution for 2x-1=10-9x^2 equation:

Simplifying
2x + -1 = 10 + -9x2

Reorder the terms:
-1 + 2x = 10 + -9x2

Solving
-1 + 2x = 10 + -9x2

Solving for variable 'x'.

Reorder the terms:
-1 + -10 + 2x + 9x2 = 10 + -9x2 + -10 + 9x2

Combine like terms: -1 + -10 = -11
-11 + 2x + 9x2 = 10 + -9x2 + -10 + 9x2

Reorder the terms:
-11 + 2x + 9x2 = 10 + -10 + -9x2 + 9x2

Combine like terms: 10 + -10 = 0
-11 + 2x + 9x2 = 0 + -9x2 + 9x2
-11 + 2x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-11 + 2x + 9x2 = 0

Factor a trinomial.
(-11 + -9x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -9x)' equal to zero and attempt to solve:

Simplifying
-11 + -9x = 0

Solving
-11 + -9x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -9x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -9x = 0 + 11
-9x = 0 + 11

Combine like terms: 0 + 11 = 11
-9x = 11

Divide each side by '-9'.
x = -1.222222222

Simplifying
x = -1.222222222
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 = {-1.222222222, 1}