0=2(x+3)(x-7)

Solution for 0=2(x+3)(x-7) equation:

Simplifying
0 = 2(x + 3)(x + -7)

Reorder the terms:
0 = 2(3 + x)(x + -7)

Reorder the terms:
0 = 2(3 + x)(-7 + x)

Multiply (3 + x) * (-7 + x)
0 = 2(3(-7 + x) + x(-7 + x))
0 = 2((-7 * 3 + x * 3) + x(-7 + x))
0 = 2((-21 + 3x) + x(-7 + x))
0 = 2(-21 + 3x + (-7 * x + x * x))
0 = 2(-21 + 3x + (-7x + x2))

Combine like terms: 3x + -7x = -4x
0 = 2(-21 + -4x + x2)
0 = (-21 * 2 + -4x * 2 + x2 * 2)
0 = (-42 + -8x + 2x2)

Solving
0 = -42 + -8x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + 8x + -2x2 = -42 + -8x + 2x2 + 42 + 8x + -2x2

Reorder the terms:
42 + 8x + -2x2 = -42 + 42 + -8x + 8x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
42 + 8x + -2x2 = 0 + -8x + 8x + 2x2 + -2x2
42 + 8x + -2x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
42 + 8x + -2x2 = 0 + 2x2 + -2x2
42 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
42 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 4x + -1x2) = 0

Factor a trinomial.
2((7 + -1x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {7, -3}