(x+5)(x+12)=60

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Solution for (x+5)(x+12)=60 equation:


Simplifying
(x + 5)(x + 12) = 60

Reorder the terms:
(5 + x)(x + 12) = 60

Reorder the terms:
(5 + x)(12 + x) = 60

Multiply (5 + x) * (12 + x)
(5(12 + x) + x(12 + x)) = 60
((12 * 5 + x * 5) + x(12 + x)) = 60
((60 + 5x) + x(12 + x)) = 60
(60 + 5x + (12 * x + x * x)) = 60
(60 + 5x + (12x + x2)) = 60

Combine like terms: 5x + 12x = 17x
(60 + 17x + x2) = 60

Add '-60' to each side of the equation.
60 + 17x + -60 + x2 = 60 + -60

Reorder the terms:
60 + -60 + 17x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
0 + 17x + x2 = 60 + -60
17x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
17x + x2 = 0

Solving
17x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(17 + x) = 0

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 '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Simplifying x = -17

Solution

x = {0, -17}

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