(x-4)(2x-10)=0

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Solution for (x-4)(2x-10)=0 equation:


Simplifying
(x + -4)(2x + -10) = 0

Reorder the terms:
(-4 + x)(2x + -10) = 0

Reorder the terms:
(-4 + x)(-10 + 2x) = 0

Multiply (-4 + x) * (-10 + 2x)
(-4(-10 + 2x) + x(-10 + 2x)) = 0
((-10 * -4 + 2x * -4) + x(-10 + 2x)) = 0
((40 + -8x) + x(-10 + 2x)) = 0
(40 + -8x + (-10 * x + 2x * x)) = 0
(40 + -8x + (-10x + 2x2)) = 0

Combine like terms: -8x + -10x = -18x
(40 + -18x + 2x2) = 0

Solving
40 + -18x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -9x + x2) = 0

Factor a trinomial.
2((4 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {4, 5}

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