(x-2)(x-10)=-16

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Solution for (x-2)(x-10)=-16 equation:


Simplifying
(x + -2)(x + -10) = -16

Reorder the terms:
(-2 + x)(x + -10) = -16

Reorder the terms:
(-2 + x)(-10 + x) = -16

Multiply (-2 + x) * (-10 + x)
(-2(-10 + x) + x(-10 + x)) = -16
((-10 * -2 + x * -2) + x(-10 + x)) = -16
((20 + -2x) + x(-10 + x)) = -16
(20 + -2x + (-10 * x + x * x)) = -16
(20 + -2x + (-10x + x2)) = -16

Combine like terms: -2x + -10x = -12x
(20 + -12x + x2) = -16

Solving
20 + -12x + x2 = -16

Solving for variable 'x'.

Reorder the terms:
20 + 16 + -12x + x2 = -16 + 16

Combine like terms: 20 + 16 = 36
36 + -12x + x2 = -16 + 16

Combine like terms: -16 + 16 = 0
36 + -12x + x2 = 0

Factor a trinomial.
(6 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {6, 6}

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