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

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


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

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

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

Multiply (5 + 3x) * (4 + -6x)
(5(4 + -6x) + 3x * (4 + -6x)) = 0
((4 * 5 + -6x * 5) + 3x * (4 + -6x)) = 0
((20 + -30x) + 3x * (4 + -6x)) = 0
(20 + -30x + (4 * 3x + -6x * 3x)) = 0
(20 + -30x + (12x + -18x2)) = 0

Combine like terms: -30x + 12x = -18x
(20 + -18x + -18x2) = 0

Solving
20 + -18x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -9x + -9x2) = 0

Factor a trinomial.
2((2 + -3x)(5 + 3x)) = 0

Ignore the factor 2.

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
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
Solution
x = {0.6666666667, -1.666666667}

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