0=-2(x-3)(x-11)

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Solution for 0=-2(x-3)(x-11) equation: 


Simplifying
0 = -2(x + -3)(x + -11)

Reorder the terms:
0 = -2(-3 + x)(x + -11)

Reorder the terms:
0 = -2(-3 + x)(-11 + x)

Multiply (-3 + x) * (-11 + x)
0 = -2(-3(-11 + x) + x(-11 + x))
0 = -2((-11 * -3 + x * -3) + x(-11 + x))
0 = -2((33 + -3x) + x(-11 + x))
0 = -2(33 + -3x + (-11 * x + x * x))
0 = -2(33 + -3x + (-11x + x2))

Combine like terms: -3x + -11x = -14x
0 = -2(33 + -14x + x2)
0 = (33 * -2 + -14x * -2 + x2 * -2)
0 = (-66 + 28x + -2x2)

Solving
0 = -66 + 28x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 66 = 66
66 + -28x + 2x2 = -66 + 28x + -2x2 + 66 + -28x + 2x2

Reorder the terms:
66 + -28x + 2x2 = -66 + 66 + 28x + -28x + -2x2 + 2x2

Combine like terms: -66 + 66 = 0
66 + -28x + 2x2 = 0 + 28x + -28x + -2x2 + 2x2
66 + -28x + 2x2 = 28x + -28x + -2x2 + 2x2

Combine like terms: 28x + -28x = 0
66 + -28x + 2x2 = 0 + -2x2 + 2x2
66 + -28x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
66 + -28x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(33 + -14x + x2) = 0

Factor a trinomial.
2((3 + -1x)(11 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {3, 11}

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