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

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


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

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

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

Multiply (-3 + 2x) * (4 + x)
(-3(4 + x) + 2x * (4 + x)) = -5
((4 * -3 + x * -3) + 2x * (4 + x)) = -5
((-12 + -3x) + 2x * (4 + x)) = -5
(-12 + -3x + (4 * 2x + x * 2x)) = -5
(-12 + -3x + (8x + 2x2)) = -5

Combine like terms: -3x + 8x = 5x
(-12 + 5x + 2x2) = -5

Solving
-12 + 5x + 2x2 = -5

Solving for variable 'x'.

Reorder the terms:
-12 + 5 + 5x + 2x2 = -5 + 5

Combine like terms: -12 + 5 = -7
-7 + 5x + 2x2 = -5 + 5

Combine like terms: -5 + 5 = 0
-7 + 5x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(1 + -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 '(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
Solution
x = {-3.5, 1}

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