x(5-x)=8(5-x)

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Solution for x(5-x)=8(5-x) equation:


Simplifying
x(5 + -1x) = 8(5 + -1x)
(5 * x + -1x * x) = 8(5 + -1x)
(5x + -1x2) = 8(5 + -1x)
5x + -1x2 = (5 * 8 + -1x * 8)
5x + -1x2 = (40 + -8x)

Solving
5x + -1x2 = 40 + -8x

Solving for variable 'x'.

Reorder the terms:
-40 + 5x + 8x + -1x2 = 40 + -8x + -40 + 8x

Combine like terms: 5x + 8x = 13x
-40 + 13x + -1x2 = 40 + -8x + -40 + 8x

Reorder the terms:
-40 + 13x + -1x2 = 40 + -40 + -8x + 8x

Combine like terms: 40 + -40 = 0
-40 + 13x + -1x2 = 0 + -8x + 8x
-40 + 13x + -1x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-40 + 13x + -1x2 = 0

Factor a trinomial.
(-8 + x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {8, 5}

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