(x-3)(2x+5)=x-15

Solution for (x-3)(2x+5)=x-15 equation:

Simplifying
(x + -3)(2x + 5) = x + -15

Reorder the terms:
(-3 + x)(2x + 5) = x + -15

Reorder the terms:
(-3 + x)(5 + 2x) = x + -15

Multiply (-3 + x) * (5 + 2x)
(-3(5 + 2x) + x(5 + 2x)) = x + -15
((5 * -3 + 2x * -3) + x(5 + 2x)) = x + -15
((-15 + -6x) + x(5 + 2x)) = x + -15
(-15 + -6x + (5 * x + 2x * x)) = x + -15
(-15 + -6x + (5x + 2x2)) = x + -15

Combine like terms: -6x + 5x = -1x
(-15 + -1x + 2x2) = x + -15

Reorder the terms:
-15 + -1x + 2x2 = -15 + x

Add '15' to each side of the equation.
-15 + -1x + 15 + 2x2 = -15 + 15 + x

Reorder the terms:
-15 + 15 + -1x + 2x2 = -15 + 15 + x

Combine like terms: -15 + 15 = 0
0 + -1x + 2x2 = -15 + 15 + x
-1x + 2x2 = -15 + 15 + x

Combine like terms: -15 + 15 = 0
-1x + 2x2 = 0 + x
-1x + 2x2 = x

Solving
-1x + 2x2 = x

Solving for variable 'x'.

Reorder the terms:
-1x + -1x + 2x2 = x + -1x

Combine like terms: -1x + -1x = -2x
-2x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + 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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}