x(8x+1)=3x^2-17x+8

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Solution for x(8x+1)=3x^2-17x+8 equation: 


Simplifying
x(8x + 1) = 3x2 + -17x + 8

Reorder the terms:
x(1 + 8x) = 3x2 + -17x + 8
(1 * x + 8x * x) = 3x2 + -17x + 8
(1x + 8x2) = 3x2 + -17x + 8

Reorder the terms:
1x + 8x2 = 8 + -17x + 3x2

Solving
1x + 8x2 = 8 + -17x + 3x2

Solving for variable 'x'.

Reorder the terms:
-8 + 1x + 17x + 8x2 + -3x2 = 8 + -17x + 3x2 + -8 + 17x + -3x2

Combine like terms: 1x + 17x = 18x
-8 + 18x + 8x2 + -3x2 = 8 + -17x + 3x2 + -8 + 17x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
-8 + 18x + 5x2 = 8 + -17x + 3x2 + -8 + 17x + -3x2

Reorder the terms:
-8 + 18x + 5x2 = 8 + -8 + -17x + 17x + 3x2 + -3x2

Combine like terms: 8 + -8 = 0
-8 + 18x + 5x2 = 0 + -17x + 17x + 3x2 + -3x2
-8 + 18x + 5x2 = -17x + 17x + 3x2 + -3x2

Combine like terms: -17x + 17x = 0
-8 + 18x + 5x2 = 0 + 3x2 + -3x2
-8 + 18x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-8 + 18x + 5x2 = 0

Factor a trinomial.
(-4 + -1x)(2 + -5x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-4, 0.4}

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