8(2x-4)=(2x+1)(x-2)

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Solution for 8(2x-4)=(2x+1)(x-2) equation: 


Simplifying
8(2x + -4) = (2x + 1)(x + -2)

Reorder the terms:
8(-4 + 2x) = (2x + 1)(x + -2)
(-4 * 8 + 2x * 8) = (2x + 1)(x + -2)
(-32 + 16x) = (2x + 1)(x + -2)

Reorder the terms:
-32 + 16x = (1 + 2x)(x + -2)

Reorder the terms:
-32 + 16x = (1 + 2x)(-2 + x)

Multiply (1 + 2x) * (-2 + x)
-32 + 16x = (1(-2 + x) + 2x * (-2 + x))
-32 + 16x = ((-2 * 1 + x * 1) + 2x * (-2 + x))
-32 + 16x = ((-2 + 1x) + 2x * (-2 + x))
-32 + 16x = (-2 + 1x + (-2 * 2x + x * 2x))
-32 + 16x = (-2 + 1x + (-4x + 2x2))

Combine like terms: 1x + -4x = -3x
-32 + 16x = (-2 + -3x + 2x2)

Solving
-32 + 16x = -2 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-32 + 2 + 16x + 3x + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

Combine like terms: -32 + 2 = -30
-30 + 16x + 3x + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

Combine like terms: 16x + 3x = 19x
-30 + 19x + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

Reorder the terms:
-30 + 19x + -2x2 = -2 + 2 + -3x + 3x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
-30 + 19x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2
-30 + 19x + -2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-30 + 19x + -2x2 = 0 + 2x2 + -2x2
-30 + 19x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-30 + 19x + -2x2 = 0

Factor a trinomial.
(-15 + 2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-15 + 2x)' equal to zero and attempt to solve:

Simplifying
-15 + 2x = 0

Solving
-15 + 2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 2x = 0 + 15
2x = 0 + 15

Combine like terms: 0 + 15 = 15
2x = 15

Divide each side by '2'.
x = 7.5

Simplifying
x = 7.5

Subproblem 2
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
Solution
x = {7.5, 2}

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