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

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


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

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

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

Multiply (-5 + x) * (3 + 2x)
(-5(3 + 2x) + x(3 + 2x)) = -15
((3 * -5 + 2x * -5) + x(3 + 2x)) = -15
((-15 + -10x) + x(3 + 2x)) = -15
(-15 + -10x + (3 * x + 2x * x)) = -15
(-15 + -10x + (3x + 2x2)) = -15

Combine like terms: -10x + 3x = -7x
(-15 + -7x + 2x2) = -15

Add '15' to each side of the equation.
-15 + -7x + 15 + 2x2 = -15 + 15

Reorder the terms:
-15 + 15 + -7x + 2x2 = -15 + 15

Combine like terms: -15 + 15 = 0
0 + -7x + 2x2 = -15 + 15
-7x + 2x2 = -15 + 15

Combine like terms: -15 + 15 = 0
-7x + 2x2 = 0

Solving
-7x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 2x) = 0


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 '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 3.5}

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