(10+2x)(22+2x)=748

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Solution for (10+2x)(22+2x)=748 equation: 


Simplifying
(10 + 2x)(22 + 2x) = 748

Multiply (10 + 2x) * (22 + 2x)
(10(22 + 2x) + 2x * (22 + 2x)) = 748
((22 * 10 + 2x * 10) + 2x * (22 + 2x)) = 748
((220 + 20x) + 2x * (22 + 2x)) = 748
(220 + 20x + (22 * 2x + 2x * 2x)) = 748
(220 + 20x + (44x + 4x2)) = 748

Combine like terms: 20x + 44x = 64x
(220 + 64x + 4x2) = 748

Solving
220 + 64x + 4x2 = 748

Solving for variable 'x'.

Reorder the terms:
220 + -748 + 64x + 4x2 = 748 + -748

Combine like terms: 220 + -748 = -528
-528 + 64x + 4x2 = 748 + -748

Combine like terms: 748 + -748 = 0
-528 + 64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-132 + 16x + x2) = 0

Factor a trinomial.
4((-22 + -1x)(6 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-22 + -1x)' equal to zero and attempt to solve:

Simplifying
-22 + -1x = 0

Solving
-22 + -1x = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x = 0 + 22
-1x = 0 + 22

Combine like terms: 0 + 22 = 22
-1x = 22

Divide each side by '-1'.
x = -22

Simplifying
x = -22

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-22, 6}

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