8(10)=(x)(24-x)

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Solution for 8(10)=(x)(24-x) equation:


Simplifying
8(10) = (x)(24 + -1x)

Multiply 8 * 10
80 = (x)(24 + -1x)
80 = (24 * x + -1x * x)
80 = (24x + -1x2)

Solving
80 = 24x + -1x2

Solving for variable 'x'.

Reorder the terms:
80 + -24x + x2 = 24x + -24x + -1x2 + x2

Combine like terms: 24x + -24x = 0
80 + -24x + x2 = 0 + -1x2 + x2
80 + -24x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
80 + -24x + x2 = 0

Factor a trinomial.
(4 + -1x)(20 + -1x) = 0

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20

Solution

x = {4, 20}

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