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

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


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

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

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

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

Combine like terms: -21x + 24x = 3x
(-24 + 3x + 21x2) = 0

Solving
-24 + 3x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + x + 7x2) = 0

Factor a trinomial.
3((-8 + -7x)(1 + -1x)) = 0

Ignore the factor 3.

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.142857143, 1}

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