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

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


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

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

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

Multiply (-4 + 3x) * (9 + 6x)
(-4(9 + 6x) + 3x * (9 + 6x)) = 0
((9 * -4 + 6x * -4) + 3x * (9 + 6x)) = 0
((-36 + -24x) + 3x * (9 + 6x)) = 0
(-36 + -24x + (9 * 3x + 6x * 3x)) = 0
(-36 + -24x + (27x + 18x2)) = 0

Combine like terms: -24x + 27x = 3x
(-36 + 3x + 18x2) = 0

Solving
-36 + 3x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + x + 6x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-1.5, 1.333333333}

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