=x(2x-3)+6(2x-3)

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


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

Reorder the terms:
0 = x(-3 + 2x) + 6(2x + -3)
0 = (-3 * x + 2x * x) + 6(2x + -3)
0 = (-3x + 2x2) + 6(2x + -3)

Reorder the terms:
0 = -3x + 2x2 + 6(-3 + 2x)
0 = -3x + 2x2 + (-3 * 6 + 2x * 6)
0 = -3x + 2x2 + (-18 + 12x)

Reorder the terms:
0 = -18 + -3x + 12x + 2x2

Combine like terms: -3x + 12x = 9x
0 = -18 + 9x + 2x2

Solving
0 = -18 + 9x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 18 = 18
18 + -9x + -2x2 = -18 + 9x + 2x2 + 18 + -9x + -2x2

Reorder the terms:
18 + -9x + -2x2 = -18 + 18 + 9x + -9x + 2x2 + -2x2

Combine like terms: -18 + 18 = 0
18 + -9x + -2x2 = 0 + 9x + -9x + 2x2 + -2x2
18 + -9x + -2x2 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 0
18 + -9x + -2x2 = 0 + 2x2 + -2x2
18 + -9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18 + -9x + -2x2 = 0

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


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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

Simplifying
x = -6
Solution
x = {1.5, -6}

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