(3x+4)(6x-5)=0

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Solution for (3x+4)(6x-5)=0 equation: 


Simplifying
(3x + 4)(6x + -5) = 0

Reorder the terms:
(4 + 3x)(6x + -5) = 0

Reorder the terms:
(4 + 3x)(-5 + 6x) = 0

Multiply (4 + 3x) * (-5 + 6x)
(4(-5 + 6x) + 3x * (-5 + 6x)) = 0
((-5 * 4 + 6x * 4) + 3x * (-5 + 6x)) = 0
((-20 + 24x) + 3x * (-5 + 6x)) = 0
(-20 + 24x + (-5 * 3x + 6x * 3x)) = 0
(-20 + 24x + (-15x + 18x2)) = 0

Combine like terms: 24x + -15x = 9x
(-20 + 9x + 18x2) = 0

Solving
-20 + 9x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(5 + -6x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
5 + -6x = 0

Solving
5 + -6x = 0

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

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

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

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

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-1.333333333, 0.8333333333}

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