(2x-27)(2x-28)=552

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Solution for (2x-27)(2x-28)=552 equation: 


Simplifying
(2x + -27)(2x + -28) = 552

Reorder the terms:
(-27 + 2x)(2x + -28) = 552

Reorder the terms:
(-27 + 2x)(-28 + 2x) = 552

Multiply (-27 + 2x) * (-28 + 2x)
(-27(-28 + 2x) + 2x * (-28 + 2x)) = 552
((-28 * -27 + 2x * -27) + 2x * (-28 + 2x)) = 552
((756 + -54x) + 2x * (-28 + 2x)) = 552
(756 + -54x + (-28 * 2x + 2x * 2x)) = 552
(756 + -54x + (-56x + 4x2)) = 552

Combine like terms: -54x + -56x = -110x
(756 + -110x + 4x2) = 552

Solving
756 + -110x + 4x2 = 552

Solving for variable 'x'.

Reorder the terms:
756 + -552 + -110x + 4x2 = 552 + -552

Combine like terms: 756 + -552 = 204
204 + -110x + 4x2 = 552 + -552

Combine like terms: 552 + -552 = 0
204 + -110x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(102 + -55x + 2x2) = 0

Factor a trinomial.
2((2 + -1x)(51 + -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 '(51 + -2x)' equal to zero and attempt to solve:

Simplifying
51 + -2x = 0

Solving
51 + -2x = 0

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

Add '-51' to each side of the equation.
51 + -51 + -2x = 0 + -51

Combine like terms: 51 + -51 = 0
0 + -2x = 0 + -51
-2x = 0 + -51

Combine like terms: 0 + -51 = -51
-2x = -51

Divide each side by '-2'.
x = 25.5

Simplifying
x = 25.5
Solution
x = {2, 25.5}

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