(5+2x)(4+2x)=110

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Solution for (5+2x)(4+2x)=110 equation: 


Simplifying
(5 + 2x)(4 + 2x) = 110

Multiply (5 + 2x) * (4 + 2x)
(5(4 + 2x) + 2x * (4 + 2x)) = 110
((4 * 5 + 2x * 5) + 2x * (4 + 2x)) = 110
((20 + 10x) + 2x * (4 + 2x)) = 110
(20 + 10x + (4 * 2x + 2x * 2x)) = 110
(20 + 10x + (8x + 4x2)) = 110

Combine like terms: 10x + 8x = 18x
(20 + 18x + 4x2) = 110

Solving
20 + 18x + 4x2 = 110

Solving for variable 'x'.

Reorder the terms:
20 + -110 + 18x + 4x2 = 110 + -110

Combine like terms: 20 + -110 = -90
-90 + 18x + 4x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-90 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 9x + 2x2) = 0

Factor a trinomial.
2((-15 + -2x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7.5, 3}

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