x(5x+2)=2x^2-2x+32

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Solution for x(5x+2)=2x^2-2x+32 equation: 


Simplifying
x(5x + 2) = 2x2 + -2x + 32

Reorder the terms:
x(2 + 5x) = 2x2 + -2x + 32
(2 * x + 5x * x) = 2x2 + -2x + 32
(2x + 5x2) = 2x2 + -2x + 32

Reorder the terms:
2x + 5x2 = 32 + -2x + 2x2

Solving
2x + 5x2 = 32 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
-32 + 2x + 2x + 5x2 + -2x2 = 32 + -2x + 2x2 + -32 + 2x + -2x2

Combine like terms: 2x + 2x = 4x
-32 + 4x + 5x2 + -2x2 = 32 + -2x + 2x2 + -32 + 2x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-32 + 4x + 3x2 = 32 + -2x + 2x2 + -32 + 2x + -2x2

Reorder the terms:
-32 + 4x + 3x2 = 32 + -32 + -2x + 2x + 2x2 + -2x2

Combine like terms: 32 + -32 = 0
-32 + 4x + 3x2 = 0 + -2x + 2x + 2x2 + -2x2
-32 + 4x + 3x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
-32 + 4x + 3x2 = 0 + 2x2 + -2x2
-32 + 4x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-32 + 4x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(8 + -3x) = 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 '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-4, 2.666666667}

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