x-1=5(x-1)(x+2)

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Solution for x-1=5(x-1)(x+2) equation:


Simplifying
x + -1 = 5(x + -1)(x + 2)

Reorder the terms:
-1 + x = 5(x + -1)(x + 2)

Reorder the terms:
-1 + x = 5(-1 + x)(x + 2)

Reorder the terms:
-1 + x = 5(-1 + x)(2 + x)

Multiply (-1 + x) * (2 + x)
-1 + x = 5(-1(2 + x) + x(2 + x))
-1 + x = 5((2 * -1 + x * -1) + x(2 + x))
-1 + x = 5((-2 + -1x) + x(2 + x))
-1 + x = 5(-2 + -1x + (2 * x + x * x))
-1 + x = 5(-2 + -1x + (2x + x2))

Combine like terms: -1x + 2x = 1x
-1 + x = 5(-2 + 1x + x2)
-1 + x = (-2 * 5 + 1x * 5 + x2 * 5)
-1 + x = (-10 + 5x + 5x2)

Solving
-1 + x = -10 + 5x + 5x2

Solving for variable 'x'.

Reorder the terms:
-1 + 10 + x + -5x + -5x2 = -10 + 5x + 5x2 + 10 + -5x + -5x2

Combine like terms: -1 + 10 = 9
9 + x + -5x + -5x2 = -10 + 5x + 5x2 + 10 + -5x + -5x2

Combine like terms: x + -5x = -4x
9 + -4x + -5x2 = -10 + 5x + 5x2 + 10 + -5x + -5x2

Reorder the terms:
9 + -4x + -5x2 = -10 + 10 + 5x + -5x + 5x2 + -5x2

Combine like terms: -10 + 10 = 0
9 + -4x + -5x2 = 0 + 5x + -5x + 5x2 + -5x2
9 + -4x + -5x2 = 5x + -5x + 5x2 + -5x2

Combine like terms: 5x + -5x = 0
9 + -4x + -5x2 = 0 + 5x2 + -5x2
9 + -4x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
9 + -4x + -5x2 = 0

Factor a trinomial.
(1 + -1x)(9 + 5x) = 0


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 '(9 + 5x)' equal to zero and attempt to solve:

Simplifying
9 + 5x = 0

Solving
9 + 5x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5x = 0 + -9
5x = 0 + -9

Combine like terms: 0 + -9 = -9
5x = -9

Divide each side by '5'.
x = -1.8

Simplifying
x = -1.8
Solution
x = {1, -1.8}

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