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

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


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

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

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

Multiply (6 + 4x) * (-4 + 6x)
(6(-4 + 6x) + 4x * (-4 + 6x)) = 0
((-4 * 6 + 6x * 6) + 4x * (-4 + 6x)) = 0
((-24 + 36x) + 4x * (-4 + 6x)) = 0
(-24 + 36x + (-4 * 4x + 6x * 4x)) = 0
(-24 + 36x + (-16x + 24x2)) = 0

Combine like terms: 36x + -16x = 20x
(-24 + 20x + 24x2) = 0

Solving
-24 + 20x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 5x + 6x2) = 0

Factor a trinomial.
4((-3 + -2x)(2 + -3x)) = 0

Ignore the factor 4.

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 '(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
Solution
x = {-1.5, 0.6666666667}

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