(4x+7)(3x+12)=0

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Solution for (4x+7)(3x+12)=0 equation: 


Simplifying
(4x + 7)(3x + 12) = 0

Reorder the terms:
(7 + 4x)(3x + 12) = 0

Reorder the terms:
(7 + 4x)(12 + 3x) = 0

Multiply (7 + 4x) * (12 + 3x)
(7(12 + 3x) + 4x * (12 + 3x)) = 0
((12 * 7 + 3x * 7) + 4x * (12 + 3x)) = 0
((84 + 21x) + 4x * (12 + 3x)) = 0
(84 + 21x + (12 * 4x + 3x * 4x)) = 0
(84 + 21x + (48x + 12x2)) = 0

Combine like terms: 21x + 48x = 69x
(84 + 69x + 12x2) = 0

Solving
84 + 69x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + 23x + 4x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4

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 = {-4, -1.75}

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