x(9x+1)=4x^2-31x+64

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Solution for x(9x+1)=4x^2-31x+64 equation: 


Simplifying
x(9x + 1) = 4x2 + -31x + 64

Reorder the terms:
x(1 + 9x) = 4x2 + -31x + 64
(1 * x + 9x * x) = 4x2 + -31x + 64
(1x + 9x2) = 4x2 + -31x + 64

Reorder the terms:
1x + 9x2 = 64 + -31x + 4x2

Solving
1x + 9x2 = 64 + -31x + 4x2

Solving for variable 'x'.

Reorder the terms:
-64 + 1x + 31x + 9x2 + -4x2 = 64 + -31x + 4x2 + -64 + 31x + -4x2

Combine like terms: 1x + 31x = 32x
-64 + 32x + 9x2 + -4x2 = 64 + -31x + 4x2 + -64 + 31x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-64 + 32x + 5x2 = 64 + -31x + 4x2 + -64 + 31x + -4x2

Reorder the terms:
-64 + 32x + 5x2 = 64 + -64 + -31x + 31x + 4x2 + -4x2

Combine like terms: 64 + -64 = 0
-64 + 32x + 5x2 = 0 + -31x + 31x + 4x2 + -4x2
-64 + 32x + 5x2 = -31x + 31x + 4x2 + -4x2

Combine like terms: -31x + 31x = 0
-64 + 32x + 5x2 = 0 + 4x2 + -4x2
-64 + 32x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-64 + 32x + 5x2 = 0

Factor a trinomial.
(-8 + -1x)(8 + -5x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-8, 1.6}

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