1=(10x^2)+9x

Solution for 1=(10x^2)+9x equation:

Simplifying
1 = (10x2) + 9x

Reorder the terms:
1 = 9x + (10x2)

Solving
1 = 9x + (10x2)

Solving for variable 'x'.

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

Combine like terms: 9x + -9x = 0
1 + -9x + (-10x2) = 0 + (10x2) + (-10x2)
1 + -9x + (-10x2) = (10x2) + (-10x2)

Combine like terms: (10x2) + (-10x2) = 0
1 + -9x + (-10x2) = 0

Factor a trinomial.
(1 + -10x)(1 + x) = 0

Subproblem 1
Set the factor '(1 + -10x)' equal to zero and attempt to solve:

Simplifying
1 + -10x = 0

Solving
1 + -10x = 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 + -10x = 0 + -1

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

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

Divide each side by '-10'.
x = 0.1

Simplifying
x = 0.1
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0.1, -1}