7(x-3)+x(x+4)=5

Solution for 7(x-3)+x(x+4)=5 equation:

Simplifying
7(x + -3) + x(x + 4) = 5

Reorder the terms:
7(-3 + x) + x(x + 4) = 5
(-3 * 7 + x * 7) + x(x + 4) = 5
(-21 + 7x) + x(x + 4) = 5

Reorder the terms:
-21 + 7x + x(4 + x) = 5
-21 + 7x + (4 * x + x * x) = 5
-21 + 7x + (4x + x2) = 5

Combine like terms: 7x + 4x = 11x
-21 + 11x + x2 = 5

Solving
-21 + 11x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-21 + -5 + 11x + x2 = 5 + -5

Combine like terms: -21 + -5 = -26
-26 + 11x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-26 + 11x + x2 = 0

Factor a trinomial.
(-13 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
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 = {-13, 2}