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

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

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

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

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

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

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

Combine like terms: -27x + 18x = -9x
0 = (27 + -9x + -18x2)

Solving
0 = 27 + -9x + -18x2

Solving for variable 'x'.

Combine like terms: 0 + -27 = -27
-27 + 9x + 18x2 = 27 + -9x + -18x2 + -27 + 9x + 18x2

Reorder the terms:
-27 + 9x + 18x2 = 27 + -27 + -9x + 9x + -18x2 + 18x2

Combine like terms: 27 + -27 = 0
-27 + 9x + 18x2 = 0 + -9x + 9x + -18x2 + 18x2
-27 + 9x + 18x2 = -9x + 9x + -18x2 + 18x2

Combine like terms: -9x + 9x = 0
-27 + 9x + 18x2 = 0 + -18x2 + 18x2
-27 + 9x + 18x2 = -18x2 + 18x2

Combine like terms: -18x2 + 18x2 = 0
-27 + 9x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + x + 2x2) = 0

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

Ignore the factor 9.
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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-1.5, 1}