(6-x)(6-x)+2x*(6-x)*(-1)=

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Solution for (6-x)(6-x)+2x*(6-x)*(-1)= equation:


Simplifying
(6 + -1x)(6 + -1x) + 2x(6 + -1x)(-1) = 0

Multiply (6 + -1x) * (6 + -1x)
(6(6 + -1x) + -1x * (6 + -1x)) + 2x(6 + -1x)(-1) = 0
((6 * 6 + -1x * 6) + -1x * (6 + -1x)) + 2x(6 + -1x)(-1) = 0
((36 + -6x) + -1x * (6 + -1x)) + 2x(6 + -1x)(-1) = 0
(36 + -6x + (6 * -1x + -1x * -1x)) + 2x(6 + -1x)(-1) = 0
(36 + -6x + (-6x + 1x2)) + 2x(6 + -1x)(-1) = 0

Combine like terms: -6x + -6x = -12x
(36 + -12x + 1x2) + 2x(6 + -1x)(-1) = 0

Reorder the terms for easier multiplication:
36 + -12x + 1x2 + 2 * -1x(6 + -1x) = 0

Multiply 2 * -1
36 + -12x + 1x2 + -2x(6 + -1x) = 0
36 + -12x + 1x2 + (6 * -2x + -1x * -2x) = 0
36 + -12x + 1x2 + (-12x + 2x2) = 0

Reorder the terms:
36 + -12x + -12x + 1x2 + 2x2 = 0

Combine like terms: -12x + -12x = -24x
36 + -24x + 1x2 + 2x2 = 0

Combine like terms: 1x2 + 2x2 = 3x2
36 + -24x + 3x2 = 0

Solving
36 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -8x + x2) = 0

Factor a trinomial.
3((2 + -1x)(6 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

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

Solution

x = {2, 6}

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