(24-2x)(19-2x)=374

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Solution for (24-2x)(19-2x)=374 equation: 


Simplifying
(24 + -2x)(19 + -2x) = 374

Multiply (24 + -2x) * (19 + -2x)
(24(19 + -2x) + -2x * (19 + -2x)) = 374
((19 * 24 + -2x * 24) + -2x * (19 + -2x)) = 374
((456 + -48x) + -2x * (19 + -2x)) = 374
(456 + -48x + (19 * -2x + -2x * -2x)) = 374
(456 + -48x + (-38x + 4x2)) = 374

Combine like terms: -48x + -38x = -86x
(456 + -86x + 4x2) = 374

Solving
456 + -86x + 4x2 = 374

Solving for variable 'x'.

Reorder the terms:
456 + -374 + -86x + 4x2 = 374 + -374

Combine like terms: 456 + -374 = 82
82 + -86x + 4x2 = 374 + -374

Combine like terms: 374 + -374 = 0
82 + -86x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(41 + -43x + 2x2) = 0

Factor a trinomial.
2((1 + -1x)(41 + -2x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(41 + -2x)' equal to zero and attempt to solve:

Simplifying
41 + -2x = 0

Solving
41 + -2x = 0

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

Add '-41' to each side of the equation.
41 + -41 + -2x = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -2x = 0 + -41
-2x = 0 + -41

Combine like terms: 0 + -41 = -41
-2x = -41

Divide each side by '-2'.
x = 20.5

Simplifying
x = 20.5
Solution
x = {1, 20.5}

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