9x(-2x+9)=8x-41

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Solution for 9x(-2x+9)=8x-41 equation: 


Simplifying
9x(-2x + 9) = 8x + -41

Reorder the terms:
9x(9 + -2x) = 8x + -41
(9 * 9x + -2x * 9x) = 8x + -41
(81x + -18x2) = 8x + -41

Reorder the terms:
81x + -18x2 = -41 + 8x

Solving
81x + -18x2 = -41 + 8x

Solving for variable 'x'.

Reorder the terms:
41 + 81x + -8x + -18x2 = -41 + 8x + 41 + -8x

Combine like terms: 81x + -8x = 73x
41 + 73x + -18x2 = -41 + 8x + 41 + -8x

Reorder the terms:
41 + 73x + -18x2 = -41 + 41 + 8x + -8x

Combine like terms: -41 + 41 = 0
41 + 73x + -18x2 = 0 + 8x + -8x
41 + 73x + -18x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
41 + 73x + -18x2 = 0

Factor a trinomial.
(41 + -9x)(1 + 2x) = 0


Subproblem 1
Set the factor '(41 + -9x)' equal to zero and attempt to solve:

Simplifying
41 + -9x = 0

Solving
41 + -9x = 0

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

Add '-41' to each side of the equation.
41 + -41 + -9x = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -9x = 0 + -41
-9x = 0 + -41

Combine like terms: 0 + -41 = -41
-9x = -41

Divide each side by '-9'.
x = 4.555555556

Simplifying
x = 4.555555556

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 = {4.555555556, -0.5}

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