45-45x=(7x+4)(x-1)

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Solution for 45-45x=(7x+4)(x-1) equation: 


Simplifying
45 + -45x = (7x + 4)(x + -1)

Reorder the terms:
45 + -45x = (4 + 7x)(x + -1)

Reorder the terms:
45 + -45x = (4 + 7x)(-1 + x)

Multiply (4 + 7x) * (-1 + x)
45 + -45x = (4(-1 + x) + 7x * (-1 + x))
45 + -45x = ((-1 * 4 + x * 4) + 7x * (-1 + x))
45 + -45x = ((-4 + 4x) + 7x * (-1 + x))
45 + -45x = (-4 + 4x + (-1 * 7x + x * 7x))
45 + -45x = (-4 + 4x + (-7x + 7x2))

Combine like terms: 4x + -7x = -3x
45 + -45x = (-4 + -3x + 7x2)

Solving
45 + -45x = -4 + -3x + 7x2

Solving for variable 'x'.

Reorder the terms:
45 + 4 + -45x + 3x + -7x2 = -4 + -3x + 7x2 + 4 + 3x + -7x2

Combine like terms: 45 + 4 = 49
49 + -45x + 3x + -7x2 = -4 + -3x + 7x2 + 4 + 3x + -7x2

Combine like terms: -45x + 3x = -42x
49 + -42x + -7x2 = -4 + -3x + 7x2 + 4 + 3x + -7x2

Reorder the terms:
49 + -42x + -7x2 = -4 + 4 + -3x + 3x + 7x2 + -7x2

Combine like terms: -4 + 4 = 0
49 + -42x + -7x2 = 0 + -3x + 3x + 7x2 + -7x2
49 + -42x + -7x2 = -3x + 3x + 7x2 + -7x2

Combine like terms: -3x + 3x = 0
49 + -42x + -7x2 = 0 + 7x2 + -7x2
49 + -42x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
49 + -42x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(7 + -6x + -1x2) = 0

Factor a trinomial.
7((1 + -1x)(7 + x)) = 0

Ignore the factor 7.

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

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {1, -7}

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