(2x+7)(12-3x)=0

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Solution for (2x+7)(12-3x)=0 equation: 


Simplifying
(2x + 7)(12 + -3x) = 0

Reorder the terms:
(7 + 2x)(12 + -3x) = 0

Multiply (7 + 2x) * (12 + -3x)
(7(12 + -3x) + 2x * (12 + -3x)) = 0
((12 * 7 + -3x * 7) + 2x * (12 + -3x)) = 0
((84 + -21x) + 2x * (12 + -3x)) = 0
(84 + -21x + (12 * 2x + -3x * 2x)) = 0
(84 + -21x + (24x + -6x2)) = 0

Combine like terms: -21x + 24x = 3x
(84 + 3x + -6x2) = 0

Solving
84 + 3x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + x + -2x2) = 0

Factor a trinomial.
3((4 + -1x)(7 + 2x)) = 0

Ignore the factor 3.

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {4, -3.5}

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