(3x+5)(6x-7)=0

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Solution for (3x+5)(6x-7)=0 equation: 


Simplifying
(3x + 5)(6x + -7) = 0

Reorder the terms:
(5 + 3x)(6x + -7) = 0

Reorder the terms:
(5 + 3x)(-7 + 6x) = 0

Multiply (5 + 3x) * (-7 + 6x)
(5(-7 + 6x) + 3x * (-7 + 6x)) = 0
((-7 * 5 + 6x * 5) + 3x * (-7 + 6x)) = 0
((-35 + 30x) + 3x * (-7 + 6x)) = 0
(-35 + 30x + (-7 * 3x + 6x * 3x)) = 0
(-35 + 30x + (-21x + 18x2)) = 0

Combine like terms: 30x + -21x = 9x
(-35 + 9x + 18x2) = 0

Solving
-35 + 9x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -3x)(7 + -6x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-1.666666667, 1.166666667}

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