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

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


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

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

Multiply (3 + -1x) * (9 + 2x)
4(3(9 + 2x) + -1x * (9 + 2x)) = 0
4((9 * 3 + 2x * 3) + -1x * (9 + 2x)) = 0
4((27 + 6x) + -1x * (9 + 2x)) = 0
4(27 + 6x + (9 * -1x + 2x * -1x)) = 0
4(27 + 6x + (-9x + -2x2)) = 0

Combine like terms: 6x + -9x = -3x
4(27 + -3x + -2x2) = 0
(27 * 4 + -3x * 4 + -2x2 * 4) = 0
(108 + -12x + -8x2) = 0

Solving
108 + -12x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + -3x + -2x2) = 0

Factor a trinomial.
4((3 + -1x)(9 + 2x)) = 0

Ignore the factor 4.

Subproblem 1
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

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

Simplifying
9 + 2x = 0

Solving
9 + 2x = 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 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {3, -4.5}

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