8x(x-1)-5=5x(x-2)

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Solution for 8x(x-1)-5=5x(x-2) equation: 


Simplifying
8x(x + -1) + -5 = 5x(x + -2)

Reorder the terms:
8x(-1 + x) + -5 = 5x(x + -2)
(-1 * 8x + x * 8x) + -5 = 5x(x + -2)
(-8x + 8x2) + -5 = 5x(x + -2)

Reorder the terms:
-5 + -8x + 8x2 = 5x(x + -2)

Reorder the terms:
-5 + -8x + 8x2 = 5x(-2 + x)
-5 + -8x + 8x2 = (-2 * 5x + x * 5x)
-5 + -8x + 8x2 = (-10x + 5x2)

Solving
-5 + -8x + 8x2 = -10x + 5x2

Solving for variable 'x'.

Reorder the terms:
-5 + -8x + 10x + 8x2 + -5x2 = -10x + 5x2 + 10x + -5x2

Combine like terms: -8x + 10x = 2x
-5 + 2x + 8x2 + -5x2 = -10x + 5x2 + 10x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-5 + 2x + 3x2 = -10x + 5x2 + 10x + -5x2

Reorder the terms:
-5 + 2x + 3x2 = -10x + 10x + 5x2 + -5x2

Combine like terms: -10x + 10x = 0
-5 + 2x + 3x2 = 0 + 5x2 + -5x2
-5 + 2x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-5 + 2x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.666666667, 1}

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