0=4(2x-1)(x+4)

Solution for 0=4(2x-1)(x+4) equation:

Simplifying
0 = 4(2x + -1)(x + 4)

Reorder the terms:
0 = 4(-1 + 2x)(x + 4)

Reorder the terms:
0 = 4(-1 + 2x)(4 + x)

Multiply (-1 + 2x) * (4 + x)
0 = 4(-1(4 + x) + 2x * (4 + x))
0 = 4((4 * -1 + x * -1) + 2x * (4 + x))
0 = 4((-4 + -1x) + 2x * (4 + x))
0 = 4(-4 + -1x + (4 * 2x + x * 2x))
0 = 4(-4 + -1x + (8x + 2x2))

Combine like terms: -1x + 8x = 7x
0 = 4(-4 + 7x + 2x2)
0 = (-4 * 4 + 7x * 4 + 2x2 * 4)
0 = (-16 + 28x + 8x2)

Solving
0 = -16 + 28x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 16 = 16
16 + -28x + -8x2 = -16 + 28x + 8x2 + 16 + -28x + -8x2

Reorder the terms:
16 + -28x + -8x2 = -16 + 16 + 28x + -28x + 8x2 + -8x2

Combine like terms: -16 + 16 = 0
16 + -28x + -8x2 = 0 + 28x + -28x + 8x2 + -8x2
16 + -28x + -8x2 = 28x + -28x + 8x2 + -8x2

Combine like terms: 28x + -28x = 0
16 + -28x + -8x2 = 0 + 8x2 + -8x2
16 + -28x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
16 + -28x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -7x + -2x2) = 0

Factor a trinomial.
4((1 + -2x)(4 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0.5, -4}