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

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

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

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

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

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

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) = 2(x + -4)(x + 4)

Reorder the terms:
-2 + 1x + x2 = 2(-4 + x)(x + 4)

Reorder the terms:
-2 + 1x + x2 = 2(-4 + x)(4 + x)

Multiply (-4 + x) * (4 + x)
-2 + 1x + x2 = 2(-4(4 + x) + x(4 + x))
-2 + 1x + x2 = 2((4 * -4 + x * -4) + x(4 + x))
-2 + 1x + x2 = 2((-16 + -4x) + x(4 + x))
-2 + 1x + x2 = 2(-16 + -4x + (4 * x + x * x))
-2 + 1x + x2 = 2(-16 + -4x + (4x + x2))

Combine like terms: -4x + 4x = 0
-2 + 1x + x2 = 2(-16 + 0 + x2)
-2 + 1x + x2 = 2(-16 + x2)
-2 + 1x + x2 = (-16 * 2 + x2 * 2)
-2 + 1x + x2 = (-32 + 2x2)

Solving
-2 + 1x + x2 = -32 + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 32 + 1x + x2 + -2x2 = -32 + 2x2 + 32 + -2x2

Combine like terms: -2 + 32 = 30
30 + 1x + x2 + -2x2 = -32 + 2x2 + 32 + -2x2

Combine like terms: x2 + -2x2 = -1x2
30 + 1x + -1x2 = -32 + 2x2 + 32 + -2x2

Reorder the terms:
30 + 1x + -1x2 = -32 + 32 + 2x2 + -2x2

Combine like terms: -32 + 32 = 0
30 + 1x + -1x2 = 0 + 2x2 + -2x2
30 + 1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
30 + 1x + -1x2 = 0

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

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
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
Solution
x = {6, -5}