(25+4x)(21+2x)=21*25+714

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Solution for (25+4x)(21+2x)=21*25+714 equation: 


Simplifying
(25 + 4x)(21 + 2x) = 21 * 25 + 714

Multiply (25 + 4x) * (21 + 2x)
(25(21 + 2x) + 4x * (21 + 2x)) = 21 * 25 + 714
((21 * 25 + 2x * 25) + 4x * (21 + 2x)) = 21 * 25 + 714
((525 + 50x) + 4x * (21 + 2x)) = 21 * 25 + 714
(525 + 50x + (21 * 4x + 2x * 4x)) = 21 * 25 + 714
(525 + 50x + (84x + 8x2)) = 21 * 25 + 714

Combine like terms: 50x + 84x = 134x
(525 + 134x + 8x2) = 21 * 25 + 714

Multiply 21 * 25
525 + 134x + 8x2 = 525 + 714

Combine like terms: 525 + 714 = 1239
525 + 134x + 8x2 = 1239

Solving
525 + 134x + 8x2 = 1239

Solving for variable 'x'.

Reorder the terms:
525 + -1239 + 134x + 8x2 = 1239 + -1239

Combine like terms: 525 + -1239 = -714
-714 + 134x + 8x2 = 1239 + -1239

Combine like terms: 1239 + -1239 = 0
-714 + 134x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-357 + 67x + 4x2) = 0

Factor a trinomial.
2((-21 + -1x)(17 + -4x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve:

Simplifying
-21 + -1x = 0

Solving
-21 + -1x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1x = 0 + 21
-1x = 0 + 21

Combine like terms: 0 + 21 = 21
-1x = 21

Divide each side by '-1'.
x = -21

Simplifying
x = -21

Subproblem 2
Set the factor '(17 + -4x)' equal to zero and attempt to solve:

Simplifying
17 + -4x = 0

Solving
17 + -4x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -4x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4x = 0 + -17
-4x = 0 + -17

Combine like terms: 0 + -17 = -17
-4x = -17

Divide each side by '-4'.
x = 4.25

Simplifying
x = 4.25
Solution
x = {-21, 4.25}

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