(54-2x)(35-2x)=1470

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Solution for (54-2x)(35-2x)=1470 equation: 


Simplifying
(54 + -2x)(35 + -2x) = 1470

Multiply (54 + -2x) * (35 + -2x)
(54(35 + -2x) + -2x * (35 + -2x)) = 1470
((35 * 54 + -2x * 54) + -2x * (35 + -2x)) = 1470
((1890 + -108x) + -2x * (35 + -2x)) = 1470
(1890 + -108x + (35 * -2x + -2x * -2x)) = 1470
(1890 + -108x + (-70x + 4x2)) = 1470

Combine like terms: -108x + -70x = -178x
(1890 + -178x + 4x2) = 1470

Solving
1890 + -178x + 4x2 = 1470

Solving for variable 'x'.

Reorder the terms:
1890 + -1470 + -178x + 4x2 = 1470 + -1470

Combine like terms: 1890 + -1470 = 420
420 + -178x + 4x2 = 1470 + -1470

Combine like terms: 1470 + -1470 = 0
420 + -178x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(210 + -89x + 2x2) = 0

Factor a trinomial.
2((5 + -2x)(42 + -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 '(42 + -1x)' equal to zero and attempt to solve:

Simplifying
42 + -1x = 0

Solving
42 + -1x = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1x = 0 + -42
-1x = 0 + -42

Combine like terms: 0 + -42 = -42
-1x = -42

Divide each side by '-1'.
x = 42

Simplifying
x = 42
Solution
x = {2.5, 42}

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