3x^2+x-1=(2x+9)(x-1)

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Solution for 3x^2+x-1=(2x+9)(x-1) equation: 


Simplifying
3x2 + x + -1 = (2x + 9)(x + -1)

Reorder the terms:
-1 + x + 3x2 = (2x + 9)(x + -1)

Reorder the terms:
-1 + x + 3x2 = (9 + 2x)(x + -1)

Reorder the terms:
-1 + x + 3x2 = (9 + 2x)(-1 + x)

Multiply (9 + 2x) * (-1 + x)
-1 + x + 3x2 = (9(-1 + x) + 2x * (-1 + x))
-1 + x + 3x2 = ((-1 * 9 + x * 9) + 2x * (-1 + x))
-1 + x + 3x2 = ((-9 + 9x) + 2x * (-1 + x))
-1 + x + 3x2 = (-9 + 9x + (-1 * 2x + x * 2x))
-1 + x + 3x2 = (-9 + 9x + (-2x + 2x2))

Combine like terms: 9x + -2x = 7x
-1 + x + 3x2 = (-9 + 7x + 2x2)

Solving
-1 + x + 3x2 = -9 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-1 + 9 + x + -7x + 3x2 + -2x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Combine like terms: -1 + 9 = 8
8 + x + -7x + 3x2 + -2x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Combine like terms: x + -7x = -6x
8 + -6x + 3x2 + -2x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
8 + -6x + 1x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Reorder the terms:
8 + -6x + 1x2 = -9 + 9 + 7x + -7x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
8 + -6x + 1x2 = 0 + 7x + -7x + 2x2 + -2x2
8 + -6x + 1x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
8 + -6x + 1x2 = 0 + 2x2 + -2x2
8 + -6x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -6x + 1x2 = 0

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


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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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