(2x+3)(x+7)=90

Solution for (2x+3)(x+7)=90 equation:

Simplifying
(2x + 3)(x + 7) = 90

Reorder the terms:
(3 + 2x)(x + 7) = 90

Reorder the terms:
(3 + 2x)(7 + x) = 90

Multiply (3 + 2x) * (7 + x)
(3(7 + x) + 2x * (7 + x)) = 90
((7 * 3 + x * 3) + 2x * (7 + x)) = 90
((21 + 3x) + 2x * (7 + x)) = 90
(21 + 3x + (7 * 2x + x * 2x)) = 90
(21 + 3x + (14x + 2x2)) = 90

Combine like terms: 3x + 14x = 17x
(21 + 17x + 2x2) = 90

Solving
21 + 17x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
21 + -90 + 17x + 2x2 = 90 + -90

Combine like terms: 21 + -90 = -69
-69 + 17x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-69 + 17x + 2x2 = 0

Factor a trinomial.
(-23 + -2x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-23 + -2x)' equal to zero and attempt to solve:

Simplifying
-23 + -2x = 0

Solving
-23 + -2x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -2x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -2x = 0 + 23
-2x = 0 + 23

Combine like terms: 0 + 23 = 23
-2x = 23

Divide each side by '-2'.
x = -11.5

Simplifying
x = -11.5
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 = {-11.5, 3}