(x-4)(x-17)=0

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Solution for (x-4)(x-17)=0 equation:


Simplifying
(x + -4)(x + -17) = 0

Reorder the terms:
(-4 + x)(x + -17) = 0

Reorder the terms:
(-4 + x)(-17 + x) = 0

Multiply (-4 + x) * (-17 + x)
(-4(-17 + x) + x(-17 + x)) = 0
((-17 * -4 + x * -4) + x(-17 + x)) = 0
((68 + -4x) + x(-17 + x)) = 0
(68 + -4x + (-17 * x + x * x)) = 0
(68 + -4x + (-17x + x2)) = 0

Combine like terms: -4x + -17x = -21x
(68 + -21x + x2) = 0

Solving
68 + -21x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(17 + -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 '(17 + -1x)' equal to zero and attempt to solve: Simplifying 17 + -1x = 0 Solving 17 + -1x = 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 + -1x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1x = 0 + -17 -1x = 0 + -17 Combine like terms: 0 + -17 = -17 -1x = -17 Divide each side by '-1'. x = 17 Simplifying x = 17

Solution

x = {4, 17}

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