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

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


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

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

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

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

Combine like terms: 20x + -18x = 2x
(-30 + 2x + 12x2) = 0

Solving
-30 + 2x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + x + 6x2) = 0

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

Ignore the factor 2.

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 '(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
Solution
x = {-1.666666667, 1.5}

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