(x-3)(x-10)=8

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Solution for (x-3)(x-10)=8 equation:


Simplifying
(x + -3)(x + -10) = 8

Reorder the terms:
(-3 + x)(x + -10) = 8

Reorder the terms:
(-3 + x)(-10 + x) = 8

Multiply (-3 + x) * (-10 + x)
(-3(-10 + x) + x(-10 + x)) = 8
((-10 * -3 + x * -3) + x(-10 + x)) = 8
((30 + -3x) + x(-10 + x)) = 8
(30 + -3x + (-10 * x + x * x)) = 8
(30 + -3x + (-10x + x2)) = 8

Combine like terms: -3x + -10x = -13x
(30 + -13x + x2) = 8

Solving
30 + -13x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
30 + -8 + -13x + x2 = 8 + -8

Combine like terms: 30 + -8 = 22
22 + -13x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
22 + -13x + x2 = 0

Factor a trinomial.
(2 + -1x)(11 + -1x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Solution

x = {2, 11}

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