(12+2x)(26+2x)=1040

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Solution for (12+2x)(26+2x)=1040 equation: 


Simplifying
(12 + 2x)(26 + 2x) = 1040

Multiply (12 + 2x) * (26 + 2x)
(12(26 + 2x) + 2x * (26 + 2x)) = 1040
((26 * 12 + 2x * 12) + 2x * (26 + 2x)) = 1040
((312 + 24x) + 2x * (26 + 2x)) = 1040
(312 + 24x + (26 * 2x + 2x * 2x)) = 1040
(312 + 24x + (52x + 4x2)) = 1040

Combine like terms: 24x + 52x = 76x
(312 + 76x + 4x2) = 1040

Solving
312 + 76x + 4x2 = 1040

Solving for variable 'x'.

Reorder the terms:
312 + -1040 + 76x + 4x2 = 1040 + -1040

Combine like terms: 312 + -1040 = -728
-728 + 76x + 4x2 = 1040 + -1040

Combine like terms: 1040 + -1040 = 0
-728 + 76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-182 + 19x + x2) = 0

Factor a trinomial.
4((-26 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve:

Simplifying
-26 + -1x = 0

Solving
-26 + -1x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x = 0 + 26
-1x = 0 + 26

Combine like terms: 0 + 26 = 26
-1x = 26

Divide each side by '-1'.
x = -26

Simplifying
x = -26

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 = {-26, 7}

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