7x(x-3)-6x(x+5)=-50

Solution for 7x(x-3)-6x(x+5)=-50 equation:

Simplifying
7x(x + -3) + -6x(x + 5) = -50

Reorder the terms:
7x(-3 + x) + -6x(x + 5) = -50
(-3 * 7x + x * 7x) + -6x(x + 5) = -50
(-21x + 7x2) + -6x(x + 5) = -50

Reorder the terms:
-21x + 7x2 + -6x(5 + x) = -50
-21x + 7x2 + (5 * -6x + x * -6x) = -50
-21x + 7x2 + (-30x + -6x2) = -50

Reorder the terms:
-21x + -30x + 7x2 + -6x2 = -50

Combine like terms: -21x + -30x = -51x
-51x + 7x2 + -6x2 = -50

Combine like terms: 7x2 + -6x2 = 1x2
-51x + 1x2 = -50

Solving
-51x + 1x2 = -50

Solving for variable 'x'.

Reorder the terms:
50 + -51x + 1x2 = -50 + 50

Combine like terms: -50 + 50 = 0
50 + -51x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(50 + -1x) = 0

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 '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {1, 50}