(3x-5)(x+3)=(3x-5)(-3x-1)

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Solution for (3x-5)(x+3)=(3x-5)(-3x-1) equation:


Simplifying
(3x + -5)(x + 3) = (3x + -5)(-3x + -1)

Reorder the terms:
(-5 + 3x)(x + 3) = (3x + -5)(-3x + -1)

Reorder the terms:
(-5 + 3x)(3 + x) = (3x + -5)(-3x + -1)

Multiply (-5 + 3x) * (3 + x)
(-5(3 + x) + 3x * (3 + x)) = (3x + -5)(-3x + -1)
((3 * -5 + x * -5) + 3x * (3 + x)) = (3x + -5)(-3x + -1)
((-15 + -5x) + 3x * (3 + x)) = (3x + -5)(-3x + -1)
(-15 + -5x + (3 * 3x + x * 3x)) = (3x + -5)(-3x + -1)
(-15 + -5x + (9x + 3x2)) = (3x + -5)(-3x + -1)

Combine like terms: -5x + 9x = 4x
(-15 + 4x + 3x2) = (3x + -5)(-3x + -1)

Reorder the terms:
-15 + 4x + 3x2 = (-5 + 3x)(-3x + -1)

Reorder the terms:
-15 + 4x + 3x2 = (-5 + 3x)(-1 + -3x)

Multiply (-5 + 3x) * (-1 + -3x)
-15 + 4x + 3x2 = (-5(-1 + -3x) + 3x * (-1 + -3x))
-15 + 4x + 3x2 = ((-1 * -5 + -3x * -5) + 3x * (-1 + -3x))
-15 + 4x + 3x2 = ((5 + 15x) + 3x * (-1 + -3x))
-15 + 4x + 3x2 = (5 + 15x + (-1 * 3x + -3x * 3x))
-15 + 4x + 3x2 = (5 + 15x + (-3x + -9x2))

Combine like terms: 15x + -3x = 12x
-15 + 4x + 3x2 = (5 + 12x + -9x2)

Solving
-15 + 4x + 3x2 = 5 + 12x + -9x2

Solving for variable 'x'.

Reorder the terms:
-15 + -5 + 4x + -12x + 3x2 + 9x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2

Combine like terms: -15 + -5 = -20
-20 + 4x + -12x + 3x2 + 9x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2

Combine like terms: 4x + -12x = -8x
-20 + -8x + 3x2 + 9x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2

Combine like terms: 3x2 + 9x2 = 12x2
-20 + -8x + 12x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2

Reorder the terms:
-20 + -8x + 12x2 = 5 + -5 + 12x + -12x + -9x2 + 9x2

Combine like terms: 5 + -5 = 0
-20 + -8x + 12x2 = 0 + 12x + -12x + -9x2 + 9x2
-20 + -8x + 12x2 = 12x + -12x + -9x2 + 9x2

Combine like terms: 12x + -12x = 0
-20 + -8x + 12x2 = 0 + -9x2 + 9x2
-20 + -8x + 12x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-20 + -8x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -2x + 3x2) = 0

Factor a trinomial.
4((-1 + -1x)(5 + -3x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {-1, 1.666666667}

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