(2x+3)*(x+7)=40

Solution for (2x+3)*(x+7)=40 equation:

Simplifying
(2x + 3)(x + 7) = 40

Reorder the terms:
(3 + 2x)(x + 7) = 40

Reorder the terms:
(3 + 2x)(7 + x) = 40

Multiply (3 + 2x) * (7 + x)
(3(7 + x) + 2x * (7 + x)) = 40
((7 * 3 + x * 3) + 2x * (7 + x)) = 40
((21 + 3x) + 2x * (7 + x)) = 40
(21 + 3x + (7 * 2x + x * 2x)) = 40
(21 + 3x + (14x + 2x2)) = 40

Combine like terms: 3x + 14x = 17x
(21 + 17x + 2x2) = 40

Solving
21 + 17x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
21 + -40 + 17x + 2x2 = 40 + -40

Combine like terms: 21 + -40 = -19
-19 + 17x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-19 + 17x + 2x2 = 0

Factor a trinomial.
(-19 + -2x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve:

Simplifying
-19 + -2x = 0

Solving
-19 + -2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x = 0 + 19
-2x = 0 + 19

Combine like terms: 0 + 19 = 19
-2x = 19

Divide each side by '-2'.
x = -9.5

Simplifying
x = -9.5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-9.5, 1}