x(9x+16)=4x^2-20x+81

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Solution for x(9x+16)=4x^2-20x+81 equation: 


Simplifying
x(9x + 16) = 4x2 + -20x + 81

Reorder the terms:
x(16 + 9x) = 4x2 + -20x + 81
(16 * x + 9x * x) = 4x2 + -20x + 81
(16x + 9x2) = 4x2 + -20x + 81

Reorder the terms:
16x + 9x2 = 81 + -20x + 4x2

Solving
16x + 9x2 = 81 + -20x + 4x2

Solving for variable 'x'.

Reorder the terms:
-81 + 16x + 20x + 9x2 + -4x2 = 81 + -20x + 4x2 + -81 + 20x + -4x2

Combine like terms: 16x + 20x = 36x
-81 + 36x + 9x2 + -4x2 = 81 + -20x + 4x2 + -81 + 20x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-81 + 36x + 5x2 = 81 + -20x + 4x2 + -81 + 20x + -4x2

Reorder the terms:
-81 + 36x + 5x2 = 81 + -81 + -20x + 20x + 4x2 + -4x2

Combine like terms: 81 + -81 = 0
-81 + 36x + 5x2 = 0 + -20x + 20x + 4x2 + -4x2
-81 + 36x + 5x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-81 + 36x + 5x2 = 0 + 4x2 + -4x2
-81 + 36x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-81 + 36x + 5x2 = 0

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


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 '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 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 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {-9, 1.8}

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