(14-2x)(19-2x)=126

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Solution for (14-2x)(19-2x)=126 equation: 


Simplifying
(14 + -2x)(19 + -2x) = 126

Multiply (14 + -2x) * (19 + -2x)
(14(19 + -2x) + -2x * (19 + -2x)) = 126
((19 * 14 + -2x * 14) + -2x * (19 + -2x)) = 126
((266 + -28x) + -2x * (19 + -2x)) = 126
(266 + -28x + (19 * -2x + -2x * -2x)) = 126
(266 + -28x + (-38x + 4x2)) = 126

Combine like terms: -28x + -38x = -66x
(266 + -66x + 4x2) = 126

Solving
266 + -66x + 4x2 = 126

Solving for variable 'x'.

Reorder the terms:
266 + -126 + -66x + 4x2 = 126 + -126

Combine like terms: 266 + -126 = 140
140 + -66x + 4x2 = 126 + -126

Combine like terms: 126 + -126 = 0
140 + -66x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(70 + -33x + 2x2) = 0

Factor a trinomial.
2((5 + -2x)(14 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {2.5, 14}

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