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

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Solution for 0=(x+5)(-2x+3) equation: 


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

Reorder the terms:
0 = (5 + x)(-2x + 3)

Reorder the terms:
0 = (5 + x)(3 + -2x)

Multiply (5 + x) * (3 + -2x)
0 = (5(3 + -2x) + x(3 + -2x))
0 = ((3 * 5 + -2x * 5) + x(3 + -2x))
0 = ((15 + -10x) + x(3 + -2x))
0 = (15 + -10x + (3 * x + -2x * x))
0 = (15 + -10x + (3x + -2x2))

Combine like terms: -10x + 3x = -7x
0 = (15 + -7x + -2x2)

Solving
0 = 15 + -7x + -2x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-5 + -1x)(3 + -2x) = 0


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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-5, 1.5}

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