(19-2x)(18-2x)=156

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Solution for (19-2x)(18-2x)=156 equation: 


Simplifying
(19 + -2x)(18 + -2x) = 156

Multiply (19 + -2x) * (18 + -2x)
(19(18 + -2x) + -2x * (18 + -2x)) = 156
((18 * 19 + -2x * 19) + -2x * (18 + -2x)) = 156
((342 + -38x) + -2x * (18 + -2x)) = 156
(342 + -38x + (18 * -2x + -2x * -2x)) = 156
(342 + -38x + (-36x + 4x2)) = 156

Combine like terms: -38x + -36x = -74x
(342 + -74x + 4x2) = 156

Solving
342 + -74x + 4x2 = 156

Solving for variable 'x'.

Reorder the terms:
342 + -156 + -74x + 4x2 = 156 + -156

Combine like terms: 342 + -156 = 186
186 + -74x + 4x2 = 156 + -156

Combine like terms: 156 + -156 = 0
186 + -74x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(93 + -37x + 2x2) = 0

Factor a trinomial.
2((3 + -1x)(31 + -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 '(31 + -2x)' equal to zero and attempt to solve:

Simplifying
31 + -2x = 0

Solving
31 + -2x = 0

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

Add '-31' to each side of the equation.
31 + -31 + -2x = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -2x = 0 + -31
-2x = 0 + -31

Combine like terms: 0 + -31 = -31
-2x = -31

Divide each side by '-2'.
x = 15.5

Simplifying
x = 15.5
Solution
x = {3, 15.5}

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