(7x-8)(3x+6)=0

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Solution for (7x-8)(3x+6)=0 equation: 


Simplifying
(7x + -8)(3x + 6) = 0

Reorder the terms:
(-8 + 7x)(3x + 6) = 0

Reorder the terms:
(-8 + 7x)(6 + 3x) = 0

Multiply (-8 + 7x) * (6 + 3x)
(-8(6 + 3x) + 7x * (6 + 3x)) = 0
((6 * -8 + 3x * -8) + 7x * (6 + 3x)) = 0
((-48 + -24x) + 7x * (6 + 3x)) = 0
(-48 + -24x + (6 * 7x + 3x * 7x)) = 0
(-48 + -24x + (42x + 21x2)) = 0

Combine like terms: -24x + 42x = 18x
(-48 + 18x + 21x2) = 0

Solving
-48 + 18x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 6x + 7x2) = 0

Factor a trinomial.
3((-2 + -1x)(8 + -7x)) = 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 '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {-2, 1.142857143}

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