(3x+8)(5x-6)=0

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Solution for (3x+8)(5x-6)=0 equation: 


Simplifying
(3x + 8)(5x + -6) = 0

Reorder the terms:
(8 + 3x)(5x + -6) = 0

Reorder the terms:
(8 + 3x)(-6 + 5x) = 0

Multiply (8 + 3x) * (-6 + 5x)
(8(-6 + 5x) + 3x * (-6 + 5x)) = 0
((-6 * 8 + 5x * 8) + 3x * (-6 + 5x)) = 0
((-48 + 40x) + 3x * (-6 + 5x)) = 0
(-48 + 40x + (-6 * 3x + 5x * 3x)) = 0
(-48 + 40x + (-18x + 15x2)) = 0

Combine like terms: 40x + -18x = 22x
(-48 + 22x + 15x2) = 0

Solving
-48 + 22x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -3x)(6 + -5x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 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 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-2.666666667, 1.2}

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