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

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


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

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

Reorder the terms for easier multiplication:
2x = (4x + 9)(x + -2)

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

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

Multiply (9 + 4x) * (-2 + x)
2x = (9(-2 + x) + 4x * (-2 + x))
2x = ((-2 * 9 + x * 9) + 4x * (-2 + x))
2x = ((-18 + 9x) + 4x * (-2 + x))
2x = (-18 + 9x + (-2 * 4x + x * 4x))
2x = (-18 + 9x + (-8x + 4x2))

Combine like terms: 9x + -8x = 1x
2x = (-18 + 1x + 4x2)

Solving
2x = -18 + 1x + 4x2

Solving for variable 'x'.

Reorder the terms:
18 + 2x + -1x + -4x2 = -18 + 1x + 4x2 + 18 + -1x + -4x2

Combine like terms: 2x + -1x = 1x
18 + 1x + -4x2 = -18 + 1x + 4x2 + 18 + -1x + -4x2

Reorder the terms:
18 + 1x + -4x2 = -18 + 18 + 1x + -1x + 4x2 + -4x2

Combine like terms: -18 + 18 = 0
18 + 1x + -4x2 = 0 + 1x + -1x + 4x2 + -4x2
18 + 1x + -4x2 = 1x + -1x + 4x2 + -4x2

Combine like terms: 1x + -1x = 0
18 + 1x + -4x2 = 0 + 4x2 + -4x2
18 + 1x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
18 + 1x + -4x2 = 0

Factor a trinomial.
(9 + -4x)(2 + x) = 0


Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {2.25, -2}

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