8x(x-2)-20=5x(x-4)

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Solution for 8x(x-2)-20=5x(x-4) equation: 


Simplifying
8x(x + -2) + -20 = 5x(x + -4)

Reorder the terms:
8x(-2 + x) + -20 = 5x(x + -4)
(-2 * 8x + x * 8x) + -20 = 5x(x + -4)
(-16x + 8x2) + -20 = 5x(x + -4)

Reorder the terms:
-20 + -16x + 8x2 = 5x(x + -4)

Reorder the terms:
-20 + -16x + 8x2 = 5x(-4 + x)
-20 + -16x + 8x2 = (-4 * 5x + x * 5x)
-20 + -16x + 8x2 = (-20x + 5x2)

Solving
-20 + -16x + 8x2 = -20x + 5x2

Solving for variable 'x'.

Reorder the terms:
-20 + -16x + 20x + 8x2 + -5x2 = -20x + 5x2 + 20x + -5x2

Combine like terms: -16x + 20x = 4x
-20 + 4x + 8x2 + -5x2 = -20x + 5x2 + 20x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-20 + 4x + 3x2 = -20x + 5x2 + 20x + -5x2

Reorder the terms:
-20 + 4x + 3x2 = -20x + 20x + 5x2 + -5x2

Combine like terms: -20x + 20x = 0
-20 + 4x + 3x2 = 0 + 5x2 + -5x2
-20 + 4x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-20 + 4x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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 = {-3.333333333, 2}

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