(16+2x)(20+2x)=1020

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Solution for (16+2x)(20+2x)=1020 equation: 


Simplifying
(16 + 2x)(20 + 2x) = 1020

Multiply (16 + 2x) * (20 + 2x)
(16(20 + 2x) + 2x * (20 + 2x)) = 1020
((20 * 16 + 2x * 16) + 2x * (20 + 2x)) = 1020
((320 + 32x) + 2x * (20 + 2x)) = 1020
(320 + 32x + (20 * 2x + 2x * 2x)) = 1020
(320 + 32x + (40x + 4x2)) = 1020

Combine like terms: 32x + 40x = 72x
(320 + 72x + 4x2) = 1020

Solving
320 + 72x + 4x2 = 1020

Solving for variable 'x'.

Reorder the terms:
320 + -1020 + 72x + 4x2 = 1020 + -1020

Combine like terms: 320 + -1020 = -700
-700 + 72x + 4x2 = 1020 + -1020

Combine like terms: 1020 + -1020 = 0
-700 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-175 + 18x + x2) = 0

Factor a trinomial.
4((-25 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + -1x)' equal to zero and attempt to solve:

Simplifying
-25 + -1x = 0

Solving
-25 + -1x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1x = 0 + 25
-1x = 0 + 25

Combine like terms: 0 + 25 = 25
-1x = 25

Divide each side by '-1'.
x = -25

Simplifying
x = -25

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 = {-25, 7}

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