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

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

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

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

Reorder the terms:
-20 + 4x = 8x(-20 + 4x)
-20 + 4x = (-20 * 8x + 4x * 8x)
-20 + 4x = (-160x + 32x2)

Solving
-20 + 4x = -160x + 32x2

Solving for variable 'x'.

Combine like terms: 4x + 160x = 164x
-20 + 164x + -32x2 = -160x + 32x2 + 160x + -32x2

Reorder the terms:
-20 + 164x + -32x2 = -160x + 160x + 32x2 + -32x2

Combine like terms: -160x + 160x = 0
-20 + 164x + -32x2 = 0 + 32x2 + -32x2
-20 + 164x + -32x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-20 + 164x + -32x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 41x + -8x2) = 0

Factor a trinomial.
4((-5 + x)(1 + -8x)) = 0

Ignore the factor 4.
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 + -8x)' equal to zero and attempt to solve:

Simplifying
1 + -8x = 0

Solving
1 + -8x = 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 + -8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8x = 0 + -1
-8x = 0 + -1

Combine like terms: 0 + -1 = -1
-8x = -1

Divide each side by '-8'.
x = 0.125

Simplifying
x = 0.125
Solution
x = {5, 0.125}