(7+3x)*(2x+5)=117

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Solution for (7+3x)*(2x+5)=117 equation: 


Simplifying
(7 + 3x)(2x + 5) = 117

Reorder the terms:
(7 + 3x)(5 + 2x) = 117

Multiply (7 + 3x) * (5 + 2x)
(7(5 + 2x) + 3x * (5 + 2x)) = 117
((5 * 7 + 2x * 7) + 3x * (5 + 2x)) = 117
((35 + 14x) + 3x * (5 + 2x)) = 117
(35 + 14x + (5 * 3x + 2x * 3x)) = 117
(35 + 14x + (15x + 6x2)) = 117

Combine like terms: 14x + 15x = 29x
(35 + 29x + 6x2) = 117

Solving
35 + 29x + 6x2 = 117

Solving for variable 'x'.

Reorder the terms:
35 + -117 + 29x + 6x2 = 117 + -117

Combine like terms: 35 + -117 = -82
-82 + 29x + 6x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-82 + 29x + 6x2 = 0

Factor a trinomial.
(-41 + -6x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-41 + -6x)' equal to zero and attempt to solve:

Simplifying
-41 + -6x = 0

Solving
-41 + -6x = 0

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

Add '41' to each side of the equation.
-41 + 41 + -6x = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -6x = 0 + 41
-6x = 0 + 41

Combine like terms: 0 + 41 = 41
-6x = 41

Divide each side by '-6'.
x = -6.833333333

Simplifying
x = -6.833333333

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6.833333333, 2}

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