(x+1)(x-7)=3x-7

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Solution for (x+1)(x-7)=3x-7 equation: 


Simplifying
(x + 1)(x + -7) = 3x + -7

Reorder the terms:
(1 + x)(x + -7) = 3x + -7

Reorder the terms:
(1 + x)(-7 + x) = 3x + -7

Multiply (1 + x) * (-7 + x)
(1(-7 + x) + x(-7 + x)) = 3x + -7
((-7 * 1 + x * 1) + x(-7 + x)) = 3x + -7
((-7 + 1x) + x(-7 + x)) = 3x + -7
(-7 + 1x + (-7 * x + x * x)) = 3x + -7
(-7 + 1x + (-7x + x2)) = 3x + -7

Combine like terms: 1x + -7x = -6x
(-7 + -6x + x2) = 3x + -7

Reorder the terms:
-7 + -6x + x2 = -7 + 3x

Add '7' to each side of the equation.
-7 + -6x + 7 + x2 = -7 + 7 + 3x

Reorder the terms:
-7 + 7 + -6x + x2 = -7 + 7 + 3x

Combine like terms: -7 + 7 = 0
0 + -6x + x2 = -7 + 7 + 3x
-6x + x2 = -7 + 7 + 3x

Combine like terms: -7 + 7 = 0
-6x + x2 = 0 + 3x
-6x + x2 = 3x

Solving
-6x + x2 = 3x

Solving for variable 'x'.

Reorder the terms:
-6x + -3x + x2 = 3x + -3x

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

Combine like terms: 3x + -3x = 0
-9x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 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 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9
Solution
x = {0, 9}

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