(6+2x)(4.5+2x)=115

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Solution for (6+2x)(4.5+2x)=115 equation: 


Simplifying
(6 + 2x)(4.5 + 2x) = 115

Multiply (6 + 2x) * (4.5 + 2x)
(6(4.5 + 2x) + 2x * (4.5 + 2x)) = 115
((4.5 * 6 + 2x * 6) + 2x * (4.5 + 2x)) = 115
((27 + 12x) + 2x * (4.5 + 2x)) = 115
(27 + 12x + (4.5 * 2x + 2x * 2x)) = 115
(27 + 12x + (9x + 4x2)) = 115

Combine like terms: 12x + 9x = 21x
(27 + 21x + 4x2) = 115

Solving
27 + 21x + 4x2 = 115

Solving for variable 'x'.

Reorder the terms:
27 + -115 + 21x + 4x2 = 115 + -115

Combine like terms: 27 + -115 = -88
-88 + 21x + 4x2 = 115 + -115

Combine like terms: 115 + -115 = 0
-88 + 21x + 4x2 = 0

Factor a trinomial.
(-8 + -1x)(11 + -4x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {-8, 2.75}

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