(4x-8)(-3x-9)=(4x-8)

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Solution for (4x-8)(-3x-9)=(4x-8) equation: 


Simplifying
(4x + -8)(-3x + -9) = (4x + -8)

Reorder the terms:
(-8 + 4x)(-3x + -9) = (4x + -8)

Reorder the terms:
(-8 + 4x)(-9 + -3x) = (4x + -8)

Multiply (-8 + 4x) * (-9 + -3x)
(-8(-9 + -3x) + 4x * (-9 + -3x)) = (4x + -8)
((-9 * -8 + -3x * -8) + 4x * (-9 + -3x)) = (4x + -8)
((72 + 24x) + 4x * (-9 + -3x)) = (4x + -8)
(72 + 24x + (-9 * 4x + -3x * 4x)) = (4x + -8)
(72 + 24x + (-36x + -12x2)) = (4x + -8)

Combine like terms: 24x + -36x = -12x
(72 + -12x + -12x2) = (4x + -8)

Reorder the terms:
72 + -12x + -12x2 = (-8 + 4x)

Remove parenthesis around (-8 + 4x)
72 + -12x + -12x2 = -8 + 4x

Solving
72 + -12x + -12x2 = -8 + 4x

Solving for variable 'x'.

Reorder the terms:
72 + 8 + -12x + -4x + -12x2 = -8 + 4x + 8 + -4x

Combine like terms: 72 + 8 = 80
80 + -12x + -4x + -12x2 = -8 + 4x + 8 + -4x

Combine like terms: -12x + -4x = -16x
80 + -16x + -12x2 = -8 + 4x + 8 + -4x

Reorder the terms:
80 + -16x + -12x2 = -8 + 8 + 4x + -4x

Combine like terms: -8 + 8 = 0
80 + -16x + -12x2 = 0 + 4x + -4x
80 + -16x + -12x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
80 + -16x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -4x + -3x2) = 0

Factor a trinomial.
4((2 + -1x)(10 + 3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(10 + 3x)' equal to zero and attempt to solve:

Simplifying
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333
Solution
x = {2, -3.333333333}

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