(x-5)x=66

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Solution for (x-5)x=66 equation:


Simplifying
(x + -5) * x = 66

Reorder the terms:
(-5 + x) * x = 66

Reorder the terms for easier multiplication:
x(-5 + x) = 66
(-5 * x + x * x) = 66
(-5x + x2) = 66

Solving
-5x + x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + -5x + x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + -5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(11 + -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 '(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 = {-6, 11}

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