6x+4=(2x-5)(9x+6)

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Solution for 6x+4=(2x-5)(9x+6) equation: 


Simplifying
6x + 4 = (2x + -5)(9x + 6)

Reorder the terms:
4 + 6x = (2x + -5)(9x + 6)

Reorder the terms:
4 + 6x = (-5 + 2x)(9x + 6)

Reorder the terms:
4 + 6x = (-5 + 2x)(6 + 9x)

Multiply (-5 + 2x) * (6 + 9x)
4 + 6x = (-5(6 + 9x) + 2x * (6 + 9x))
4 + 6x = ((6 * -5 + 9x * -5) + 2x * (6 + 9x))
4 + 6x = ((-30 + -45x) + 2x * (6 + 9x))
4 + 6x = (-30 + -45x + (6 * 2x + 9x * 2x))
4 + 6x = (-30 + -45x + (12x + 18x2))

Combine like terms: -45x + 12x = -33x
4 + 6x = (-30 + -33x + 18x2)

Solving
4 + 6x = -30 + -33x + 18x2

Solving for variable 'x'.

Reorder the terms:
4 + 30 + 6x + 33x + -18x2 = -30 + -33x + 18x2 + 30 + 33x + -18x2

Combine like terms: 4 + 30 = 34
34 + 6x + 33x + -18x2 = -30 + -33x + 18x2 + 30 + 33x + -18x2

Combine like terms: 6x + 33x = 39x
34 + 39x + -18x2 = -30 + -33x + 18x2 + 30 + 33x + -18x2

Reorder the terms:
34 + 39x + -18x2 = -30 + 30 + -33x + 33x + 18x2 + -18x2

Combine like terms: -30 + 30 = 0
34 + 39x + -18x2 = 0 + -33x + 33x + 18x2 + -18x2
34 + 39x + -18x2 = -33x + 33x + 18x2 + -18x2

Combine like terms: -33x + 33x = 0
34 + 39x + -18x2 = 0 + 18x2 + -18x2
34 + 39x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
34 + 39x + -18x2 = 0

Factor a trinomial.
(17 + -6x)(2 + 3x) = 0


Subproblem 1
Set the factor '(17 + -6x)' equal to zero and attempt to solve:

Simplifying
17 + -6x = 0

Solving
17 + -6x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -6x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -6x = 0 + -17
-6x = 0 + -17

Combine like terms: 0 + -17 = -17
-6x = -17

Divide each side by '-6'.
x = 2.833333333

Simplifying
x = 2.833333333

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {2.833333333, -0.6666666667}

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