4x(x-4)+2=x^2+2(2x+17)

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Solution for 4x(x-4)+2=x^2+2(2x+17) equation: 


Simplifying
4x(x + -4) + 2 = x2 + 2(2x + 17)

Reorder the terms:
4x(-4 + x) + 2 = x2 + 2(2x + 17)
(-4 * 4x + x * 4x) + 2 = x2 + 2(2x + 17)
(-16x + 4x2) + 2 = x2 + 2(2x + 17)

Reorder the terms:
2 + -16x + 4x2 = x2 + 2(2x + 17)

Reorder the terms:
2 + -16x + 4x2 = x2 + 2(17 + 2x)
2 + -16x + 4x2 = x2 + (17 * 2 + 2x * 2)
2 + -16x + 4x2 = x2 + (34 + 4x)

Reorder the terms:
2 + -16x + 4x2 = 34 + 4x + x2

Solving
2 + -16x + 4x2 = 34 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
2 + -34 + -16x + -4x + 4x2 + -1x2 = 34 + 4x + x2 + -34 + -4x + -1x2

Combine like terms: 2 + -34 = -32
-32 + -16x + -4x + 4x2 + -1x2 = 34 + 4x + x2 + -34 + -4x + -1x2

Combine like terms: -16x + -4x = -20x
-32 + -20x + 4x2 + -1x2 = 34 + 4x + x2 + -34 + -4x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-32 + -20x + 3x2 = 34 + 4x + x2 + -34 + -4x + -1x2

Reorder the terms:
-32 + -20x + 3x2 = 34 + -34 + 4x + -4x + x2 + -1x2

Combine like terms: 34 + -34 = 0
-32 + -20x + 3x2 = 0 + 4x + -4x + x2 + -1x2
-32 + -20x + 3x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-32 + -20x + 3x2 = 0 + x2 + -1x2
-32 + -20x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-32 + -20x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
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
Solution
x = {-1.333333333, 8}

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