(8-2x)(10-2x)=24

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Solution for (8-2x)(10-2x)=24 equation: 


Simplifying
(8 + -2x)(10 + -2x) = 24

Multiply (8 + -2x) * (10 + -2x)
(8(10 + -2x) + -2x * (10 + -2x)) = 24
((10 * 8 + -2x * 8) + -2x * (10 + -2x)) = 24
((80 + -16x) + -2x * (10 + -2x)) = 24
(80 + -16x + (10 * -2x + -2x * -2x)) = 24
(80 + -16x + (-20x + 4x2)) = 24

Combine like terms: -16x + -20x = -36x
(80 + -36x + 4x2) = 24

Solving
80 + -36x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
80 + -24 + -36x + 4x2 = 24 + -24

Combine like terms: 80 + -24 = 56
56 + -36x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
56 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + -9x + x2) = 0

Factor a trinomial.
4((2 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}

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