(4x+2)(3x-9)=0

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Solution for (4x+2)(3x-9)=0 equation: 


Simplifying
(4x + 2)(3x + -9) = 0

Reorder the terms:
(2 + 4x)(3x + -9) = 0

Reorder the terms:
(2 + 4x)(-9 + 3x) = 0

Multiply (2 + 4x) * (-9 + 3x)
(2(-9 + 3x) + 4x * (-9 + 3x)) = 0
((-9 * 2 + 3x * 2) + 4x * (-9 + 3x)) = 0
((-18 + 6x) + 4x * (-9 + 3x)) = 0
(-18 + 6x + (-9 * 4x + 3x * 4x)) = 0
(-18 + 6x + (-36x + 12x2)) = 0

Combine like terms: 6x + -36x = -30x
(-18 + -30x + 12x2) = 0

Solving
-18 + -30x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -5x + 2x2) = 0

Factor a trinomial.
6((-1 + -2x)(3 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}

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