(3x-2)(7x+8)=0

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Solution for (3x-2)(7x+8)=0 equation: 


Simplifying
(3x + -2)(7x + 8) = 0

Reorder the terms:
(-2 + 3x)(7x + 8) = 0

Reorder the terms:
(-2 + 3x)(8 + 7x) = 0

Multiply (-2 + 3x) * (8 + 7x)
(-2(8 + 7x) + 3x * (8 + 7x)) = 0
((8 * -2 + 7x * -2) + 3x * (8 + 7x)) = 0
((-16 + -14x) + 3x * (8 + 7x)) = 0
(-16 + -14x + (8 * 3x + 7x * 3x)) = 0
(-16 + -14x + (24x + 21x2)) = 0

Combine like terms: -14x + 24x = 10x
(-16 + 10x + 21x2) = 0

Solving
-16 + 10x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -7x)(2 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1.142857143, 0.6666666667}

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