(14-2x)(19-2x)=104

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Solution for (14-2x)(19-2x)=104 equation:


Simplifying
(14 + -2x)(19 + -2x) = 104

Multiply (14 + -2x) * (19 + -2x)
(14(19 + -2x) + -2x * (19 + -2x)) = 104
((19 * 14 + -2x * 14) + -2x * (19 + -2x)) = 104
((266 + -28x) + -2x * (19 + -2x)) = 104
(266 + -28x + (19 * -2x + -2x * -2x)) = 104
(266 + -28x + (-38x + 4x2)) = 104

Combine like terms: -28x + -38x = -66x
(266 + -66x + 4x2) = 104

Solving
266 + -66x + 4x2 = 104

Solving for variable 'x'.

Reorder the terms:
266 + -104 + -66x + 4x2 = 104 + -104

Combine like terms: 266 + -104 = 162
162 + -66x + 4x2 = 104 + -104

Combine like terms: 104 + -104 = 0
162 + -66x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(81 + -33x + 2x2) = 0

Factor a trinomial.
2((3 + -1x)(27 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(27 + -2x)' equal to zero and attempt to solve:

Simplifying
27 + -2x = 0

Solving
27 + -2x = 0

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

Add '-27' to each side of the equation.
27 + -27 + -2x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -2x = 0 + -27
-2x = 0 + -27

Combine like terms: 0 + -27 = -27
-2x = -27

Divide each side by '-2'.
x = 13.5

Simplifying
x = 13.5
Solution
x = {3, 13.5}

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