(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 + -1x + 6x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {-1.5, 1.666666667}

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