x(x+3)-4(x-5)=7(x+4)-8

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Solution for x(x+3)-4(x-5)=7(x+4)-8 equation: 


Simplifying
x(x + 3) + -4(x + -5) = 7(x + 4) + -8

Reorder the terms:
x(3 + x) + -4(x + -5) = 7(x + 4) + -8
(3 * x + x * x) + -4(x + -5) = 7(x + 4) + -8
(3x + x2) + -4(x + -5) = 7(x + 4) + -8

Reorder the terms:
3x + x2 + -4(-5 + x) = 7(x + 4) + -8
3x + x2 + (-5 * -4 + x * -4) = 7(x + 4) + -8
3x + x2 + (20 + -4x) = 7(x + 4) + -8

Reorder the terms:
20 + 3x + -4x + x2 = 7(x + 4) + -8

Combine like terms: 3x + -4x = -1x
20 + -1x + x2 = 7(x + 4) + -8

Reorder the terms:
20 + -1x + x2 = 7(4 + x) + -8
20 + -1x + x2 = (4 * 7 + x * 7) + -8
20 + -1x + x2 = (28 + 7x) + -8

Reorder the terms:
20 + -1x + x2 = 28 + -8 + 7x

Combine like terms: 28 + -8 = 20
20 + -1x + x2 = 20 + 7x

Add '-20' to each side of the equation.
20 + -1x + -20 + x2 = 20 + -20 + 7x

Reorder the terms:
20 + -20 + -1x + x2 = 20 + -20 + 7x

Combine like terms: 20 + -20 = 0
0 + -1x + x2 = 20 + -20 + 7x
-1x + x2 = 20 + -20 + 7x

Combine like terms: 20 + -20 = 0
-1x + x2 = 0 + 7x
-1x + x2 = 7x

Solving
-1x + x2 = 7x

Solving for variable 'x'.

Reorder the terms:
-1x + -7x + x2 = 7x + -7x

Combine like terms: -1x + -7x = -8x
-8x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-8x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 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 '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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