(x+3)(x+4)=12

Solution for (x+3)(x+4)=12 equation:

Simplifying
(x + 3)(x + 4) = 12

Reorder the terms:
(3 + x)(x + 4) = 12

Reorder the terms:
(3 + x)(4 + x) = 12

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) = 12
((4 * 3 + x * 3) + x(4 + x)) = 12
((12 + 3x) + x(4 + x)) = 12
(12 + 3x + (4 * x + x * x)) = 12
(12 + 3x + (4x + x2)) = 12

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) = 12

Add '-12' to each side of the equation.
12 + 7x + -12 + x2 = 12 + -12

Reorder the terms:
12 + -12 + 7x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
0 + 7x + x2 = 12 + -12
7x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
7x + x2 = 0

Solving
7x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0, -7}