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

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

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

Combine like terms: 5 + 7 = 12
5(12) = x(4 + x)

Multiply 5 * 12
60 = x(4 + x)
60 = (4 * x + x * x)
60 = (4x + x2)

Solving
60 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
60 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
60 + -4x + -1x2 = 0 + x2 + -1x2
60 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + -4x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(10 + x) = 0

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {6, -10}