-45x^2+22x+13=10

Solution for -45x^2+22x+13=10 equation:

Simplifying
-45x2 + 22x + 13 = 10

Reorder the terms:
13 + 22x + -45x2 = 10

Solving
13 + 22x + -45x2 = 10

Solving for variable 'x'.

Reorder the terms:
13 + -10 + 22x + -45x2 = 10 + -10

Combine like terms: 13 + -10 = 3
3 + 22x + -45x2 = 10 + -10

Combine like terms: 10 + -10 = 0
3 + 22x + -45x2 = 0

Factor a trinomial.
(3 + -5x)(1 + 9x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 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 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Solution
x = {0.6, -0.1111111111}