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

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


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

Multiply 4 * 9
36 = (x + -2)(x + -2 + x + 4)

Reorder the terms:
36 = (-2 + x)(x + -2 + x + 4)

Reorder the terms:
36 = (-2 + x)(-2 + 4 + x + x)

Combine like terms: -2 + 4 = 2
36 = (-2 + x)(2 + x + x)

Combine like terms: x + x = 2x
36 = (-2 + x)(2 + 2x)

Multiply (-2 + x) * (2 + 2x)
36 = (-2(2 + 2x) + x(2 + 2x))
36 = ((2 * -2 + 2x * -2) + x(2 + 2x))
36 = ((-4 + -4x) + x(2 + 2x))
36 = (-4 + -4x + (2 * x + 2x * x))
36 = (-4 + -4x + (2x + 2x2))

Combine like terms: -4x + 2x = -2x
36 = (-4 + -2x + 2x2)

Solving
36 = -4 + -2x + 2x2

Solving for variable 'x'.

Combine like terms: 36 + 4 = 40
40 + 2x + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2

Reorder the terms:
40 + 2x + -2x2 = -4 + 4 + -2x + 2x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
40 + 2x + -2x2 = 0 + -2x + 2x + 2x2 + -2x2
40 + 2x + -2x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
40 + 2x + -2x2 = 0 + 2x2 + -2x2
40 + 2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
40 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(4 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4
Solution
x = {5, -4}

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