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

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


Simplifying
2(3 + -1x)(4x + -9) = 0

Reorder the terms:
2(3 + -1x)(-9 + 4x) = 0

Multiply (3 + -1x) * (-9 + 4x)
2(3(-9 + 4x) + -1x * (-9 + 4x)) = 0
2((-9 * 3 + 4x * 3) + -1x * (-9 + 4x)) = 0
2((-27 + 12x) + -1x * (-9 + 4x)) = 0
2(-27 + 12x + (-9 * -1x + 4x * -1x)) = 0
2(-27 + 12x + (9x + -4x2)) = 0

Combine like terms: 12x + 9x = 21x
2(-27 + 21x + -4x2) = 0
(-27 * 2 + 21x * 2 + -4x2 * 2) = 0
(-54 + 42x + -8x2) = 0

Solving
-54 + 42x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 21x + -4x2) = 0

Factor a trinomial.
2((-3 + x)(9 + -4x)) = 0

Ignore the factor 2.

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

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {3, 2.25}

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