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

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


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

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

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

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

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

Solving
10 = 18x + 4x2

Solving for variable 'x'.

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

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

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

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

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

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

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