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

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


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

Reorder the terms:
4x(-3 + 2x) + -3(2x + -3) = 0
(-3 * 4x + 2x * 4x) + -3(2x + -3) = 0
(-12x + 8x2) + -3(2x + -3) = 0

Reorder the terms:
-12x + 8x2 + -3(-3 + 2x) = 0
-12x + 8x2 + (-3 * -3 + 2x * -3) = 0
-12x + 8x2 + (9 + -6x) = 0

Reorder the terms:
9 + -12x + -6x + 8x2 = 0

Combine like terms: -12x + -6x = -18x
9 + -18x + 8x2 = 0

Solving
9 + -18x + 8x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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 = {0.75, 1.5}

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