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 = 5x
7 + -7x = (-9 + 5x + 4x2)

Solving
7 + -7x = -9 + 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
7 + 9 + -7x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Combine like terms: 7 + 9 = 16
16 + -7x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Combine like terms: -7x + -5x = -12x
16 + -12x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2

Reorder the terms:
16 + -12x + -4x2 = -9 + 9 + 5x + -5x + 4x2 + -4x2

Combine like terms: -9 + 9 = 0
16 + -12x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
16 + -12x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
16 + -12x + -4x2 = 0 + 4x2 + -4x2
16 + -12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
16 + -12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -3x + -1x2) = 0

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

Ignore the factor 4.

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {1, -4}

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