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

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


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

Reorder the terms:
(7 + 2x)(3x + -12) = 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 + -1x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-3.5, 4}

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