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

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


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

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

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

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

Combine like terms: -24x + -21x = -45x
(84 + -45x + 6x2) = 0

Solving
84 + -45x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + -15x + 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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