(x-5)(2x+3)+4(x-5)=0

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Solution for (x-5)(2x+3)+4(x-5)=0 equation: 


Simplifying
(x + -5)(2x + 3) + 4(x + -5) = 0

Reorder the terms:
(-5 + x)(2x + 3) + 4(x + -5) = 0

Reorder the terms:
(-5 + x)(3 + 2x) + 4(x + -5) = 0

Multiply (-5 + x) * (3 + 2x)
(-5(3 + 2x) + x(3 + 2x)) + 4(x + -5) = 0
((3 * -5 + 2x * -5) + x(3 + 2x)) + 4(x + -5) = 0
((-15 + -10x) + x(3 + 2x)) + 4(x + -5) = 0
(-15 + -10x + (3 * x + 2x * x)) + 4(x + -5) = 0
(-15 + -10x + (3x + 2x2)) + 4(x + -5) = 0

Combine like terms: -10x + 3x = -7x
(-15 + -7x + 2x2) + 4(x + -5) = 0

Reorder the terms:
-15 + -7x + 2x2 + 4(-5 + x) = 0
-15 + -7x + 2x2 + (-5 * 4 + x * 4) = 0
-15 + -7x + 2x2 + (-20 + 4x) = 0

Reorder the terms:
-15 + -20 + -7x + 4x + 2x2 = 0

Combine like terms: -15 + -20 = -35
-35 + -7x + 4x + 2x2 = 0

Combine like terms: -7x + 4x = -3x
-35 + -3x + 2x2 = 0

Solving
-35 + -3x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -2x)(5 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-3.5, 5}

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