4(6x-3)(2x+9)=0

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Solution for 4(6x-3)(2x+9)=0 equation: 


Simplifying
4(6x + -3)(2x + 9) = 0

Reorder the terms:
4(-3 + 6x)(2x + 9) = 0

Reorder the terms:
4(-3 + 6x)(9 + 2x) = 0

Multiply (-3 + 6x) * (9 + 2x)
4(-3(9 + 2x) + 6x * (9 + 2x)) = 0
4((9 * -3 + 2x * -3) + 6x * (9 + 2x)) = 0
4((-27 + -6x) + 6x * (9 + 2x)) = 0
4(-27 + -6x + (9 * 6x + 2x * 6x)) = 0
4(-27 + -6x + (54x + 12x2)) = 0

Combine like terms: -6x + 54x = 48x
4(-27 + 48x + 12x2) = 0
(-27 * 4 + 48x * 4 + 12x2 * 4) = 0
(-108 + 192x + 48x2) = 0

Solving
-108 + 192x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-9 + 16x + 4x2) = 0

Factor a trinomial.
12((-9 + -2x)(1 + -2x)) = 0

Ignore the factor 12.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-4.5, 0.5}

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