(19-2x)(18-2x)=110

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Solution for (19-2x)(18-2x)=110 equation: 


Simplifying
(19 + -2x)(18 + -2x) = 110

Multiply (19 + -2x) * (18 + -2x)
(19(18 + -2x) + -2x * (18 + -2x)) = 110
((18 * 19 + -2x * 19) + -2x * (18 + -2x)) = 110
((342 + -38x) + -2x * (18 + -2x)) = 110
(342 + -38x + (18 * -2x + -2x * -2x)) = 110
(342 + -38x + (-36x + 4x2)) = 110

Combine like terms: -38x + -36x = -74x
(342 + -74x + 4x2) = 110

Solving
342 + -74x + 4x2 = 110

Solving for variable 'x'.

Reorder the terms:
342 + -110 + -74x + 4x2 = 110 + -110

Combine like terms: 342 + -110 = 232
232 + -74x + 4x2 = 110 + -110

Combine like terms: 110 + -110 = 0
232 + -74x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(116 + -37x + 2x2) = 0

Factor a trinomial.
2((4 + -1x)(29 + -2x)) = 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 '(29 + -2x)' equal to zero and attempt to solve:

Simplifying
29 + -2x = 0

Solving
29 + -2x = 0

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

Add '-29' to each side of the equation.
29 + -29 + -2x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -2x = 0 + -29
-2x = 0 + -29

Combine like terms: 0 + -29 = -29
-2x = -29

Divide each side by '-2'.
x = 14.5

Simplifying
x = 14.5
Solution
x = {4, 14.5}

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