0=-16(x-7)(x+1)

Solution for 0=-16(x-7)(x+1) equation:

Simplifying
0 = -16(x + -7)(x + 1)

Reorder the terms:
0 = -16(-7 + x)(x + 1)

Reorder the terms:
0 = -16(-7 + x)(1 + x)

Multiply (-7 + x) * (1 + x)
0 = -16(-7(1 + x) + x(1 + x))
0 = -16((1 * -7 + x * -7) + x(1 + x))
0 = -16((-7 + -7x) + x(1 + x))
0 = -16(-7 + -7x + (1 * x + x * x))
0 = -16(-7 + -7x + (1x + x2))

Combine like terms: -7x + 1x = -6x
0 = -16(-7 + -6x + x2)
0 = (-7 * -16 + -6x * -16 + x2 * -16)
0 = (112 + 96x + -16x2)

Solving
0 = 112 + 96x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -112 = -112
-112 + -96x + 16x2 = 112 + 96x + -16x2 + -112 + -96x + 16x2

Reorder the terms:
-112 + -96x + 16x2 = 112 + -112 + 96x + -96x + -16x2 + 16x2

Combine like terms: 112 + -112 = 0
-112 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2
-112 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2

Combine like terms: 96x + -96x = 0
-112 + -96x + 16x2 = 0 + -16x2 + 16x2
-112 + -96x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-112 + -96x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-7 + -6x + x2) = 0

Factor a trinomial.
16((-1 + -1x)(7 + -1x)) = 0

Ignore the factor 16.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}