(28-2x)(33-2x)=546

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Solution for (28-2x)(33-2x)=546 equation: 


Simplifying
(28 + -2x)(33 + -2x) = 546

Multiply (28 + -2x) * (33 + -2x)
(28(33 + -2x) + -2x * (33 + -2x)) = 546
((33 * 28 + -2x * 28) + -2x * (33 + -2x)) = 546
((924 + -56x) + -2x * (33 + -2x)) = 546
(924 + -56x + (33 * -2x + -2x * -2x)) = 546
(924 + -56x + (-66x + 4x2)) = 546

Combine like terms: -56x + -66x = -122x
(924 + -122x + 4x2) = 546

Solving
924 + -122x + 4x2 = 546

Solving for variable 'x'.

Reorder the terms:
924 + -546 + -122x + 4x2 = 546 + -546

Combine like terms: 924 + -546 = 378
378 + -122x + 4x2 = 546 + -546

Combine like terms: 546 + -546 = 0
378 + -122x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(189 + -61x + 2x2) = 0

Factor a trinomial.
2((7 + -2x)(27 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
Set the factor '(27 + -1x)' equal to zero and attempt to solve:

Simplifying
27 + -1x = 0

Solving
27 + -1x = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1x = 0 + -27
-1x = 0 + -27

Combine like terms: 0 + -27 = -27
-1x = -27

Divide each side by '-1'.
x = 27

Simplifying
x = 27
Solution
x = {3.5, 27}

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