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

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


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

Reorder the terms:
8x(-5 + x) = (2x + 5)(x + -5)
(-5 * 8x + x * 8x) = (2x + 5)(x + -5)
(-40x + 8x2) = (2x + 5)(x + -5)

Reorder the terms:
-40x + 8x2 = (5 + 2x)(x + -5)

Reorder the terms:
-40x + 8x2 = (5 + 2x)(-5 + x)

Multiply (5 + 2x) * (-5 + x)
-40x + 8x2 = (5(-5 + x) + 2x * (-5 + x))
-40x + 8x2 = ((-5 * 5 + x * 5) + 2x * (-5 + x))
-40x + 8x2 = ((-25 + 5x) + 2x * (-5 + x))
-40x + 8x2 = (-25 + 5x + (-5 * 2x + x * 2x))
-40x + 8x2 = (-25 + 5x + (-10x + 2x2))

Combine like terms: 5x + -10x = -5x
-40x + 8x2 = (-25 + -5x + 2x2)

Solving
-40x + 8x2 = -25 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
25 + -40x + 5x + 8x2 + -2x2 = -25 + -5x + 2x2 + 25 + 5x + -2x2

Combine like terms: -40x + 5x = -35x
25 + -35x + 8x2 + -2x2 = -25 + -5x + 2x2 + 25 + 5x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
25 + -35x + 6x2 = -25 + -5x + 2x2 + 25 + 5x + -2x2

Reorder the terms:
25 + -35x + 6x2 = -25 + 25 + -5x + 5x + 2x2 + -2x2

Combine like terms: -25 + 25 = 0
25 + -35x + 6x2 = 0 + -5x + 5x + 2x2 + -2x2
25 + -35x + 6x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
25 + -35x + 6x2 = 0 + 2x2 + -2x2
25 + -35x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
25 + -35x + 6x2 = 0

Factor a trinomial.
(5 + -6x)(5 + -1x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.8333333333, 5}

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