(5-3x)(-4x+6)=(8x+11)-(3x-6)

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Solution for (5-3x)(-4x+6)=(8x+11)-(3x-6) equation:


Simplifying
(5 + -3x)(-4x + 6) = (8x + 11) + -1(3x + -6)

Reorder the terms:
(5 + -3x)(6 + -4x) = (8x + 11) + -1(3x + -6)

Multiply (5 + -3x) * (6 + -4x)
(5(6 + -4x) + -3x * (6 + -4x)) = (8x + 11) + -1(3x + -6)
((6 * 5 + -4x * 5) + -3x * (6 + -4x)) = (8x + 11) + -1(3x + -6)
((30 + -20x) + -3x * (6 + -4x)) = (8x + 11) + -1(3x + -6)
(30 + -20x + (6 * -3x + -4x * -3x)) = (8x + 11) + -1(3x + -6)
(30 + -20x + (-18x + 12x2)) = (8x + 11) + -1(3x + -6)

Combine like terms: -20x + -18x = -38x
(30 + -38x + 12x2) = (8x + 11) + -1(3x + -6)

Reorder the terms:
30 + -38x + 12x2 = (11 + 8x) + -1(3x + -6)

Remove parenthesis around (11 + 8x)
30 + -38x + 12x2 = 11 + 8x + -1(3x + -6)

Reorder the terms:
30 + -38x + 12x2 = 11 + 8x + -1(-6 + 3x)
30 + -38x + 12x2 = 11 + 8x + (-6 * -1 + 3x * -1)
30 + -38x + 12x2 = 11 + 8x + (6 + -3x)

Reorder the terms:
30 + -38x + 12x2 = 11 + 6 + 8x + -3x

Combine like terms: 11 + 6 = 17
30 + -38x + 12x2 = 17 + 8x + -3x

Combine like terms: 8x + -3x = 5x
30 + -38x + 12x2 = 17 + 5x

Solving
30 + -38x + 12x2 = 17 + 5x

Solving for variable 'x'.

Reorder the terms:
30 + -17 + -38x + -5x + 12x2 = 17 + 5x + -17 + -5x

Combine like terms: 30 + -17 = 13
13 + -38x + -5x + 12x2 = 17 + 5x + -17 + -5x

Combine like terms: -38x + -5x = -43x
13 + -43x + 12x2 = 17 + 5x + -17 + -5x

Reorder the terms:
13 + -43x + 12x2 = 17 + -17 + 5x + -5x

Combine like terms: 17 + -17 = 0
13 + -43x + 12x2 = 0 + 5x + -5x
13 + -43x + 12x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
13 + -43x + 12x2 = 0

Factor a trinomial.
(1 + -3x)(13 + -4x) = 0


Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
Set the factor '(13 + -4x)' equal to zero and attempt to solve:

Simplifying
13 + -4x = 0

Solving
13 + -4x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4x = 0 + -13
-4x = 0 + -13

Combine like terms: 0 + -13 = -13
-4x = -13

Divide each side by '-4'.
x = 3.25

Simplifying
x = 3.25
Solution
x = {0.3333333333, 3.25}

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