(50+5x)(24-x)=1200

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Solution for (50+5x)(24-x)=1200 equation:


Simplifying
(50 + 5x)(24 + -1x) = 1200

Multiply (50 + 5x) * (24 + -1x)
(50(24 + -1x) + 5x * (24 + -1x)) = 1200
((24 * 50 + -1x * 50) + 5x * (24 + -1x)) = 1200
((1200 + -50x) + 5x * (24 + -1x)) = 1200
(1200 + -50x + (24 * 5x + -1x * 5x)) = 1200
(1200 + -50x + (120x + -5x2)) = 1200

Combine like terms: -50x + 120x = 70x
(1200 + 70x + -5x2) = 1200

Add '-1200' to each side of the equation.
1200 + 70x + -1200 + -5x2 = 1200 + -1200

Reorder the terms:
1200 + -1200 + 70x + -5x2 = 1200 + -1200

Combine like terms: 1200 + -1200 = 0
0 + 70x + -5x2 = 1200 + -1200
70x + -5x2 = 1200 + -1200

Combine like terms: 1200 + -1200 = 0
70x + -5x2 = 0

Solving
70x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(14 + -1x) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14

Solution

x = {0, 14}

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