7-7x=(4x-9)(x-1)

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Solution for 7-7x=(4x-9)(x-1) equation: 


Simplifying
7 + -7x = (4x + -9)(x + -1)

Reorder the terms:
7 + -7x = (-9 + 4x)(x + -1)

Reorder the terms:
7 + -7x = (-9 + 4x)(-1 + x)

Multiply (-9 + 4x) * (-1 + x)
7 + -7x = (-9(-1 + x) + 4x * (-1 + x))
7 + -7x = ((-1 * -9 + x * -9) + 4x * (-1 + x))
7 + -7x = ((9 + -9x) + 4x * (-1 + x))
7 + -7x = (9 + -9x + (-1 * 4x + x * 4x))
7 + -7x = (9 + -9x + (-4x + 4x2))

Combine like terms: -9x + -4x = -13x
7 + -7x = (9 + -13x + 4x2)

Solving
7 + -7x = 9 + -13x + 4x2

Solving for variable 'x'.

Reorder the terms:
7 + -9 + -7x + 13x + -4x2 = 9 + -13x + 4x2 + -9 + 13x + -4x2

Combine like terms: 7 + -9 = -2
-2 + -7x + 13x + -4x2 = 9 + -13x + 4x2 + -9 + 13x + -4x2

Combine like terms: -7x + 13x = 6x
-2 + 6x + -4x2 = 9 + -13x + 4x2 + -9 + 13x + -4x2

Reorder the terms:
-2 + 6x + -4x2 = 9 + -9 + -13x + 13x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
-2 + 6x + -4x2 = 0 + -13x + 13x + 4x2 + -4x2
-2 + 6x + -4x2 = -13x + 13x + 4x2 + -4x2

Combine like terms: -13x + 13x = 0
-2 + 6x + -4x2 = 0 + 4x2 + -4x2
-2 + 6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2 + 6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3x + -2x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {1, 0.5}

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