4(2x-10)=8x(x-5)

Solution for 4(2x-10)=8x(x-5) equation:

Simplifying
4(2x + -10) = 8x(x + -5)

Reorder the terms:
4(-10 + 2x) = 8x(x + -5)
(-10 * 4 + 2x * 4) = 8x(x + -5)
(-40 + 8x) = 8x(x + -5)

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

Solving
-40 + 8x = -40x + 8x2

Solving for variable 'x'.

Combine like terms: 8x + 40x = 48x
-40 + 48x + -8x2 = -40x + 8x2 + 40x + -8x2

Reorder the terms:
-40 + 48x + -8x2 = -40x + 40x + 8x2 + -8x2

Combine like terms: -40x + 40x = 0
-40 + 48x + -8x2 = 0 + 8x2 + -8x2
-40 + 48x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-40 + 48x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-5 + 6x + -1x2) = 0

Factor a trinomial.
8((-5 + x)(1 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

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

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

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

Simplifying
x = 5
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 = {5, 1}