(3x+9)(4x+7)=

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Solution for (3x+9)(4x+7)= equation: 


Simplifying
(3x + 9)(4x + 7) = 0

Reorder the terms:
(9 + 3x)(4x + 7) = 0

Reorder the terms:
(9 + 3x)(7 + 4x) = 0

Multiply (9 + 3x) * (7 + 4x)
(9(7 + 4x) + 3x * (7 + 4x)) = 0
((7 * 9 + 4x * 9) + 3x * (7 + 4x)) = 0
((63 + 36x) + 3x * (7 + 4x)) = 0
(63 + 36x + (7 * 3x + 4x * 3x)) = 0
(63 + 36x + (21x + 12x2)) = 0

Combine like terms: 36x + 21x = 57x
(63 + 57x + 12x2) = 0

Solving
63 + 57x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + 19x + 4x2) = 0

Factor a trinomial.
3((3 + x)(7 + 4x)) = 0

Ignore the factor 3.

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {-3, -1.75}

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