(2x+16)(2x+26)=1200

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Solution for (2x+16)(2x+26)=1200 equation: 


Simplifying
(2x + 16)(2x + 26) = 1200

Reorder the terms:
(16 + 2x)(2x + 26) = 1200

Reorder the terms:
(16 + 2x)(26 + 2x) = 1200

Multiply (16 + 2x) * (26 + 2x)
(16(26 + 2x) + 2x * (26 + 2x)) = 1200
((26 * 16 + 2x * 16) + 2x * (26 + 2x)) = 1200
((416 + 32x) + 2x * (26 + 2x)) = 1200
(416 + 32x + (26 * 2x + 2x * 2x)) = 1200
(416 + 32x + (52x + 4x2)) = 1200

Combine like terms: 32x + 52x = 84x
(416 + 84x + 4x2) = 1200

Solving
416 + 84x + 4x2 = 1200

Solving for variable 'x'.

Reorder the terms:
416 + -1200 + 84x + 4x2 = 1200 + -1200

Combine like terms: 416 + -1200 = -784
-784 + 84x + 4x2 = 1200 + -1200

Combine like terms: 1200 + -1200 = 0
-784 + 84x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-196 + 21x + x2) = 0

Factor a trinomial.
4((-28 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-28 + -1x)' equal to zero and attempt to solve:

Simplifying
-28 + -1x = 0

Solving
-28 + -1x = 0

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

Add '28' to each side of the equation.
-28 + 28 + -1x = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -1x = 0 + 28
-1x = 0 + 28

Combine like terms: 0 + 28 = 28
-1x = 28

Divide each side by '-1'.
x = -28

Simplifying
x = -28

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-28, 7}

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