(7x-8)(3x+1)=0

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Solution for (7x-8)(3x+1)=0 equation: 


Simplifying
(7x + -8)(3x + 1) = 0

Reorder the terms:
(-8 + 7x)(3x + 1) = 0

Reorder the terms:
(-8 + 7x)(1 + 3x) = 0

Multiply (-8 + 7x) * (1 + 3x)
(-8(1 + 3x) + 7x * (1 + 3x)) = 0
((1 * -8 + 3x * -8) + 7x * (1 + 3x)) = 0
((-8 + -24x) + 7x * (1 + 3x)) = 0
(-8 + -24x + (1 * 7x + 3x * 7x)) = 0
(-8 + -24x + (7x + 21x2)) = 0

Combine like terms: -24x + 7x = -17x
(-8 + -17x + 21x2) = 0

Solving
-8 + -17x + 21x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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 = {-0.3333333333, 1.142857143}

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