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

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


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

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

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

Multiply (3 + 2x) * (4 + 3x)
0 = (3(4 + 3x) + 2x * (4 + 3x))
0 = ((4 * 3 + 3x * 3) + 2x * (4 + 3x))
0 = ((12 + 9x) + 2x * (4 + 3x))
0 = (12 + 9x + (4 * 2x + 3x * 2x))
0 = (12 + 9x + (8x + 6x2))

Combine like terms: 9x + 8x = 17x
0 = (12 + 17x + 6x2)

Solving
0 = 12 + 17x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + -17x + -6x2 = 12 + 17x + 6x2 + -12 + -17x + -6x2

Reorder the terms:
-12 + -17x + -6x2 = 12 + -12 + 17x + -17x + 6x2 + -6x2

Combine like terms: 12 + -12 = 0
-12 + -17x + -6x2 = 0 + 17x + -17x + 6x2 + -6x2
-12 + -17x + -6x2 = 17x + -17x + 6x2 + -6x2

Combine like terms: 17x + -17x = 0
-12 + -17x + -6x2 = 0 + 6x2 + -6x2
-12 + -17x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-12 + -17x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 17x + 6x2) = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, -1.333333333}

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