(4+2x)(5+2x)=56

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Solution for (4+2x)(5+2x)=56 equation: 


Simplifying
(4 + 2x)(5 + 2x) = 56

Multiply (4 + 2x) * (5 + 2x)
(4(5 + 2x) + 2x * (5 + 2x)) = 56
((5 * 4 + 2x * 4) + 2x * (5 + 2x)) = 56
((20 + 8x) + 2x * (5 + 2x)) = 56
(20 + 8x + (5 * 2x + 2x * 2x)) = 56
(20 + 8x + (10x + 4x2)) = 56

Combine like terms: 8x + 10x = 18x
(20 + 18x + 4x2) = 56

Solving
20 + 18x + 4x2 = 56

Solving for variable 'x'.

Reorder the terms:
20 + -56 + 18x + 4x2 = 56 + -56

Combine like terms: 20 + -56 = -36
-36 + 18x + 4x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-36 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 9x + 2x2) = 0

Factor a trinomial.
2((-6 + -1x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-6, 1.5}

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