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

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


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

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

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

Combine like terms: x + -3x = -2x
(9 + 6x)(4 + -2x) = 0

Multiply (9 + 6x) * (4 + -2x)
(9(4 + -2x) + 6x * (4 + -2x)) = 0
((4 * 9 + -2x * 9) + 6x * (4 + -2x)) = 0
((36 + -18x) + 6x * (4 + -2x)) = 0
(36 + -18x + (4 * 6x + -2x * 6x)) = 0
(36 + -18x + (24x + -12x2)) = 0

Combine like terms: -18x + 24x = 6x
(36 + 6x + -12x2) = 0

Solving
36 + 6x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + x + -2x2) = 0

Factor a trinomial.
6((2 + -1x)(3 + 2x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, -1.5}

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