(6-x)(7-x)=0

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Solution for (6-x)(7-x)=0 equation:


Simplifying
(6 + -1x)(7 + -1x) = 0

Multiply (6 + -1x) * (7 + -1x)
(6(7 + -1x) + -1x * (7 + -1x)) = 0
((7 * 6 + -1x * 6) + -1x * (7 + -1x)) = 0
((42 + -6x) + -1x * (7 + -1x)) = 0
(42 + -6x + (7 * -1x + -1x * -1x)) = 0
(42 + -6x + (-7x + 1x2)) = 0

Combine like terms: -6x + -7x = -13x
(42 + -13x + 1x2) = 0

Solving
42 + -13x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(7 + -1x) = 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 '(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 = {6, 7}

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