x(5x+12)=2x^2-4x+64

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Solution for x(5x+12)=2x^2-4x+64 equation: 


Simplifying
x(5x + 12) = 2x2 + -4x + 64

Reorder the terms:
x(12 + 5x) = 2x2 + -4x + 64
(12 * x + 5x * x) = 2x2 + -4x + 64
(12x + 5x2) = 2x2 + -4x + 64

Reorder the terms:
12x + 5x2 = 64 + -4x + 2x2

Solving
12x + 5x2 = 64 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-64 + 12x + 4x + 5x2 + -2x2 = 64 + -4x + 2x2 + -64 + 4x + -2x2

Combine like terms: 12x + 4x = 16x
-64 + 16x + 5x2 + -2x2 = 64 + -4x + 2x2 + -64 + 4x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-64 + 16x + 3x2 = 64 + -4x + 2x2 + -64 + 4x + -2x2

Reorder the terms:
-64 + 16x + 3x2 = 64 + -64 + -4x + 4x + 2x2 + -2x2

Combine like terms: 64 + -64 = 0
-64 + 16x + 3x2 = 0 + -4x + 4x + 2x2 + -2x2
-64 + 16x + 3x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
-64 + 16x + 3x2 = 0 + 2x2 + -2x2
-64 + 16x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-64 + 16x + 3x2 = 0

Factor a trinomial.
(-8 + -1x)(8 + -3x) = 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 + -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 = {-8, 2.666666667}

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