(3x+6)(x-1)=(x+1)(x+9)

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Solution for (3x+6)(x-1)=(x+1)(x+9) equation:


Simplifying
(3x + 6)(x + -1) = (x + 1)(x + 9)

Reorder the terms:
(6 + 3x)(x + -1) = (x + 1)(x + 9)

Reorder the terms:
(6 + 3x)(-1 + x) = (x + 1)(x + 9)

Multiply (6 + 3x) * (-1 + x)
(6(-1 + x) + 3x * (-1 + x)) = (x + 1)(x + 9)
((-1 * 6 + x * 6) + 3x * (-1 + x)) = (x + 1)(x + 9)
((-6 + 6x) + 3x * (-1 + x)) = (x + 1)(x + 9)
(-6 + 6x + (-1 * 3x + x * 3x)) = (x + 1)(x + 9)
(-6 + 6x + (-3x + 3x2)) = (x + 1)(x + 9)

Combine like terms: 6x + -3x = 3x
(-6 + 3x + 3x2) = (x + 1)(x + 9)

Reorder the terms:
-6 + 3x + 3x2 = (1 + x)(x + 9)

Reorder the terms:
-6 + 3x + 3x2 = (1 + x)(9 + x)

Multiply (1 + x) * (9 + x)
-6 + 3x + 3x2 = (1(9 + x) + x(9 + x))
-6 + 3x + 3x2 = ((9 * 1 + x * 1) + x(9 + x))
-6 + 3x + 3x2 = ((9 + 1x) + x(9 + x))
-6 + 3x + 3x2 = (9 + 1x + (9 * x + x * x))
-6 + 3x + 3x2 = (9 + 1x + (9x + x2))

Combine like terms: 1x + 9x = 10x
-6 + 3x + 3x2 = (9 + 10x + x2)

Solving
-6 + 3x + 3x2 = 9 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + -9 + 3x + -10x + 3x2 + -1x2 = 9 + 10x + x2 + -9 + -10x + -1x2

Combine like terms: -6 + -9 = -15
-15 + 3x + -10x + 3x2 + -1x2 = 9 + 10x + x2 + -9 + -10x + -1x2

Combine like terms: 3x + -10x = -7x
-15 + -7x + 3x2 + -1x2 = 9 + 10x + x2 + -9 + -10x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-15 + -7x + 2x2 = 9 + 10x + x2 + -9 + -10x + -1x2

Reorder the terms:
-15 + -7x + 2x2 = 9 + -9 + 10x + -10x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-15 + -7x + 2x2 = 0 + 10x + -10x + x2 + -1x2
-15 + -7x + 2x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-15 + -7x + 2x2 = 0 + x2 + -1x2
-15 + -7x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + -7x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

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

Solution

x = {-1.5, 5}

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