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

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


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

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

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

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

Combine like terms: -16x + 21x = 5x
(-24 + 5x + 14x2) = 0

Solving
-24 + 5x + 14x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 1.142857143}

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