x(x-7)+3x=3x^2+8x

Solution for x(x-7)+3x=3x^2+8x equation:

Simplifying
x(x + -7) + 3x = 3x2 + 8x

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

Reorder the terms:
-7x + 3x + x2 = 3x2 + 8x

Combine like terms: -7x + 3x = -4x
-4x + x2 = 3x2 + 8x

Reorder the terms:
-4x + x2 = 8x + 3x2

Solving
-4x + x2 = 8x + 3x2

Solving for variable 'x'.

Reorder the terms:
-4x + -8x + x2 + -3x2 = 8x + 3x2 + -8x + -3x2

Combine like terms: -4x + -8x = -12x
-12x + x2 + -3x2 = 8x + 3x2 + -8x + -3x2

Combine like terms: x2 + -3x2 = -2x2
-12x + -2x2 = 8x + 3x2 + -8x + -3x2

Reorder the terms:
-12x + -2x2 = 8x + -8x + 3x2 + -3x2

Combine like terms: 8x + -8x = 0
-12x + -2x2 = 0 + 3x2 + -3x2
-12x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(6 + x) = 0

Ignore the factor -2.
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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0, -6}