(4+2x)(5+2x)-20=10

Solution for (4+2x)(5+2x)-20=10 equation:

Simplifying
(4 + 2x)(5 + 2x) + -20 = 10

Multiply (4 + 2x) * (5 + 2x)
(4(5 + 2x) + 2x * (5 + 2x)) + -20 = 10
((5 * 4 + 2x * 4) + 2x * (5 + 2x)) + -20 = 10
((20 + 8x) + 2x * (5 + 2x)) + -20 = 10
(20 + 8x + (5 * 2x + 2x * 2x)) + -20 = 10
(20 + 8x + (10x + 4x2)) + -20 = 10

Combine like terms: 8x + 10x = 18x
(20 + 18x + 4x2) + -20 = 10

Reorder the terms:
20 + -20 + 18x + 4x2 = 10

Combine like terms: 20 + -20 = 0
0 + 18x + 4x2 = 10
18x + 4x2 = 10

Solving
18x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 18x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 9x + 2x2) = 0

Factor a trinomial.
2((-5 + -1x)(1 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-5, 0.5}