(2x-7)(3x+6)=0

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Solution for (2x-7)(3x+6)=0 equation: 


Simplifying
(2x + -7)(3x + 6) = 0

Reorder the terms:
(-7 + 2x)(3x + 6) = 0

Reorder the terms:
(-7 + 2x)(6 + 3x) = 0

Multiply (-7 + 2x) * (6 + 3x)
(-7(6 + 3x) + 2x * (6 + 3x)) = 0
((6 * -7 + 3x * -7) + 2x * (6 + 3x)) = 0
((-42 + -21x) + 2x * (6 + 3x)) = 0
(-42 + -21x + (6 * 2x + 3x * 2x)) = 0
(-42 + -21x + (12x + 6x2)) = 0

Combine like terms: -21x + 12x = -9x
(-42 + -9x + 6x2) = 0

Solving
-42 + -9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -3x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 3.5}

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