7x(x-1)=(2x+9)(x-1)

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Solution for 7x(x-1)=(2x+9)(x-1) equation: 


Simplifying
7x(x + -1) = (2x + 9)(x + -1)

Reorder the terms:
7x(-1 + x) = (2x + 9)(x + -1)
(-1 * 7x + x * 7x) = (2x + 9)(x + -1)
(-7x + 7x2) = (2x + 9)(x + -1)

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

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

Multiply (9 + 2x) * (-1 + x)
-7x + 7x2 = (9(-1 + x) + 2x * (-1 + x))
-7x + 7x2 = ((-1 * 9 + x * 9) + 2x * (-1 + x))
-7x + 7x2 = ((-9 + 9x) + 2x * (-1 + x))
-7x + 7x2 = (-9 + 9x + (-1 * 2x + x * 2x))
-7x + 7x2 = (-9 + 9x + (-2x + 2x2))

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

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

Solving for variable 'x'.

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

Combine like terms: -7x + -7x = -14x
9 + -14x + 7x2 + -2x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
9 + -14x + 5x2 = -9 + 7x + 2x2 + 9 + -7x + -2x2

Reorder the terms:
9 + -14x + 5x2 = -9 + 9 + 7x + -7x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
9 + -14x + 5x2 = 0 + 7x + -7x + 2x2 + -2x2
9 + -14x + 5x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
9 + -14x + 5x2 = 0 + 2x2 + -2x2
9 + -14x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
9 + -14x + 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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