x(8x+4)=3x^2-32x+81

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Solution for x(8x+4)=3x^2-32x+81 equation: 


Simplifying
x(8x + 4) = 3x2 + -32x + 81

Reorder the terms:
x(4 + 8x) = 3x2 + -32x + 81
(4 * x + 8x * x) = 3x2 + -32x + 81
(4x + 8x2) = 3x2 + -32x + 81

Reorder the terms:
4x + 8x2 = 81 + -32x + 3x2

Solving
4x + 8x2 = 81 + -32x + 3x2

Solving for variable 'x'.

Reorder the terms:
-81 + 4x + 32x + 8x2 + -3x2 = 81 + -32x + 3x2 + -81 + 32x + -3x2

Combine like terms: 4x + 32x = 36x
-81 + 36x + 8x2 + -3x2 = 81 + -32x + 3x2 + -81 + 32x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
-81 + 36x + 5x2 = 81 + -32x + 3x2 + -81 + 32x + -3x2

Reorder the terms:
-81 + 36x + 5x2 = 81 + -81 + -32x + 32x + 3x2 + -3x2

Combine like terms: 81 + -81 = 0
-81 + 36x + 5x2 = 0 + -32x + 32x + 3x2 + -3x2
-81 + 36x + 5x2 = -32x + 32x + 3x2 + -3x2

Combine like terms: -32x + 32x = 0
-81 + 36x + 5x2 = 0 + 3x2 + -3x2
-81 + 36x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 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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