(14-2x)(19-2x)=150

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Solution for (14-2x)(19-2x)=150 equation: 


Simplifying
(14 + -2x)(19 + -2x) = 150

Multiply (14 + -2x) * (19 + -2x)
(14(19 + -2x) + -2x * (19 + -2x)) = 150
((19 * 14 + -2x * 14) + -2x * (19 + -2x)) = 150
((266 + -28x) + -2x * (19 + -2x)) = 150
(266 + -28x + (19 * -2x + -2x * -2x)) = 150
(266 + -28x + (-38x + 4x2)) = 150

Combine like terms: -28x + -38x = -66x
(266 + -66x + 4x2) = 150

Solving
266 + -66x + 4x2 = 150

Solving for variable 'x'.

Reorder the terms:
266 + -150 + -66x + 4x2 = 150 + -150

Combine like terms: 266 + -150 = 116
116 + -66x + 4x2 = 150 + -150

Combine like terms: 150 + -150 = 0
116 + -66x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(58 + -33x + 2x2) = 0

Factor a trinomial.
2((2 + -1x)(29 + -2x)) = 0

Ignore the factor 2.

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 '(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 = {2, 14.5}

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