=(x+2)(3x+4)

Solution for =(x+2)(3x+4) equation:

Simplifying
0 = (x + 2)(3x + 4)

Reorder the terms:
0 = (2 + x)(3x + 4)

Reorder the terms:
0 = (2 + x)(4 + 3x)

Multiply (2 + x) * (4 + 3x)
0 = (2(4 + 3x) + x(4 + 3x))
0 = ((4 * 2 + 3x * 2) + x(4 + 3x))
0 = ((8 + 6x) + x(4 + 3x))
0 = (8 + 6x + (4 * x + 3x * x))
0 = (8 + 6x + (4x + 3x2))

Combine like terms: 6x + 4x = 10x
0 = (8 + 10x + 3x2)

Solving
0 = 8 + 10x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -10x + -3x2 = 8 + 10x + 3x2 + -8 + -10x + -3x2

Reorder the terms:
-8 + -10x + -3x2 = 8 + -8 + 10x + -10x + 3x2 + -3x2

Combine like terms: 8 + -8 = 0
-8 + -10x + -3x2 = 0 + 10x + -10x + 3x2 + -3x2
-8 + -10x + -3x2 = 10x + -10x + 3x2 + -3x2

Combine like terms: 10x + -10x = 0
-8 + -10x + -3x2 = 0 + 3x2 + -3x2
-8 + -10x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-8 + -10x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 10x + 3x2) = 0

Factor a trinomial.
-1((2 + x)(4 + 3x)) = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-2, -1.333333333}