5x^2+17x-18=6-9x

Solution for 5x^2+17x-18=6-9x equation:

Simplifying
5x2 + 17x + -18 = 6 + -9x

Reorder the terms:
-18 + 17x + 5x2 = 6 + -9x

Solving
-18 + 17x + 5x2 = 6 + -9x

Solving for variable 'x'.

Reorder the terms:
-18 + -6 + 17x + 9x + 5x2 = 6 + -9x + -6 + 9x

Combine like terms: -18 + -6 = -24
-24 + 17x + 9x + 5x2 = 6 + -9x + -6 + 9x

Combine like terms: 17x + 9x = 26x
-24 + 26x + 5x2 = 6 + -9x + -6 + 9x

Reorder the terms:
-24 + 26x + 5x2 = 6 + -6 + -9x + 9x

Combine like terms: 6 + -6 = 0
-24 + 26x + 5x2 = 0 + -9x + 9x
-24 + 26x + 5x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-24 + 26x + 5x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -5x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-6, 0.8}