10x^2+85x=45

Solution for 10x^2+85x=45 equation:

Simplifying
10x2 + 85x = 45

Reorder the terms:
85x + 10x2 = 45

Solving
85x + 10x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + 85x + 10x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 85x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + 17x + 2x2) = 0

Factor a trinomial.
5((-9 + -1x)(1 + -2x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

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

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

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 0.5}