(v-7)(v-6)=0

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


Simplifying
(v + -7)(v + -6) = 0

Reorder the terms:
(-7 + v)(v + -6) = 0

Reorder the terms:
(-7 + v)(-6 + v) = 0

Multiply (-7 + v) * (-6 + v)
(-7(-6 + v) + v(-6 + v)) = 0
((-6 * -7 + v * -7) + v(-6 + v)) = 0
((42 + -7v) + v(-6 + v)) = 0
(42 + -7v + (-6 * v + v * v)) = 0
(42 + -7v + (-6v + v2)) = 0

Combine like terms: -7v + -6v = -13v
(42 + -13v + v2) = 0

Solving
42 + -13v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + -1v)(7 + -1v) = 0

Subproblem 1

Set the factor '(6 + -1v)' equal to zero and attempt to solve: Simplifying 6 + -1v = 0 Solving 6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1v = 0 + -6 -1v = 0 + -6 Combine like terms: 0 + -6 = -6 -1v = -6 Divide each side by '-1'. v = 6 Simplifying v = 6

Subproblem 2

Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7

Solution

v = {6, 7}

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