5x(x-3)+6=5x-9

Solution for 5x(x-3)+6=5x-9 equation:

Simplifying
5x(x + -3) + 6 = 5x + -9

Reorder the terms:
5x(-3 + x) + 6 = 5x + -9
(-3 * 5x + x * 5x) + 6 = 5x + -9
(-15x + 5x2) + 6 = 5x + -9

Reorder the terms:
6 + -15x + 5x2 = 5x + -9

Reorder the terms:
6 + -15x + 5x2 = -9 + 5x

Solving
6 + -15x + 5x2 = -9 + 5x

Solving for variable 'x'.

Reorder the terms:
6 + 9 + -15x + -5x + 5x2 = -9 + 5x + 9 + -5x

Combine like terms: 6 + 9 = 15
15 + -15x + -5x + 5x2 = -9 + 5x + 9 + -5x

Combine like terms: -15x + -5x = -20x
15 + -20x + 5x2 = -9 + 5x + 9 + -5x

Reorder the terms:
15 + -20x + 5x2 = -9 + 9 + 5x + -5x

Combine like terms: -9 + 9 = 0
15 + -20x + 5x2 = 0 + 5x + -5x
15 + -20x + 5x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
15 + -20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + -4x + x2) = 0

Factor a trinomial.
5((1 + -1x)(3 + -1x)) = 0

Ignore the factor 5.
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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}