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

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


Simplifying
x(8x + 2) = 3x2 + -4x + 8

Reorder the terms:
x(2 + 8x) = 3x2 + -4x + 8
(2 * x + 8x * x) = 3x2 + -4x + 8
(2x + 8x2) = 3x2 + -4x + 8

Reorder the terms:
2x + 8x2 = 8 + -4x + 3x2

Solving
2x + 8x2 = 8 + -4x + 3x2

Solving for variable 'x'.

Reorder the terms:
-8 + 2x + 4x + 8x2 + -3x2 = 8 + -4x + 3x2 + -8 + 4x + -3x2

Combine like terms: 2x + 4x = 6x
-8 + 6x + 8x2 + -3x2 = 8 + -4x + 3x2 + -8 + 4x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
-8 + 6x + 5x2 = 8 + -4x + 3x2 + -8 + 4x + -3x2

Reorder the terms:
-8 + 6x + 5x2 = 8 + -8 + -4x + 4x + 3x2 + -3x2

Combine like terms: 8 + -8 = 0
-8 + 6x + 5x2 = 0 + -4x + 4x + 3x2 + -3x2
-8 + 6x + 5x2 = -4x + 4x + 3x2 + -3x2

Combine like terms: -4x + 4x = 0
-8 + 6x + 5x2 = 0 + 3x2 + -3x2
-8 + 6x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-8 + 6x + 5x2 = 0

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


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-2, 0.8}

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