5x(x+6)-2x=3(x+10)

Solution for 5x(x+6)-2x=3(x+10) equation:

Simplifying
5x(x + 6) + -2x = 3(x + 10)

Reorder the terms:
5x(6 + x) + -2x = 3(x + 10)
(6 * 5x + x * 5x) + -2x = 3(x + 10)
(30x + 5x2) + -2x = 3(x + 10)

Reorder the terms:
30x + -2x + 5x2 = 3(x + 10)

Combine like terms: 30x + -2x = 28x
28x + 5x2 = 3(x + 10)

Reorder the terms:
28x + 5x2 = 3(10 + x)
28x + 5x2 = (10 * 3 + x * 3)
28x + 5x2 = (30 + 3x)

Solving
28x + 5x2 = 30 + 3x

Solving for variable 'x'.

Reorder the terms:
-30 + 28x + -3x + 5x2 = 30 + 3x + -30 + -3x

Combine like terms: 28x + -3x = 25x
-30 + 25x + 5x2 = 30 + 3x + -30 + -3x

Reorder the terms:
-30 + 25x + 5x2 = 30 + -30 + 3x + -3x

Combine like terms: 30 + -30 = 0
-30 + 25x + 5x2 = 0 + 3x + -3x
-30 + 25x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-30 + 25x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 5x + x2) = 0

Factor a trinomial.
5((-6 + -1x)(1 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
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
Solution
x = {-6, 1}