(x+7)(x+10)=130

Solution for (x+7)(x+10)=130 equation:

Simplifying
(x + 7)(x + 10) = 130

Reorder the terms:
(7 + x)(x + 10) = 130

Reorder the terms:
(7 + x)(10 + x) = 130

Multiply (7 + x) * (10 + x)
(7(10 + x) + x(10 + x)) = 130
((10 * 7 + x * 7) + x(10 + x)) = 130
((70 + 7x) + x(10 + x)) = 130
(70 + 7x + (10 * x + x * x)) = 130
(70 + 7x + (10x + x2)) = 130

Combine like terms: 7x + 10x = 17x
(70 + 17x + x2) = 130

Solving
70 + 17x + x2 = 130

Solving for variable 'x'.

Reorder the terms:
70 + -130 + 17x + x2 = 130 + -130

Combine like terms: 70 + -130 = -60
-60 + 17x + x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-60 + 17x + x2 = 0

Factor a trinomial.
(-20 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
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 = {-20, 3}