(2x+3)(x-4)=13

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Solution for (2x+3)(x-4)=13 equation: 


Simplifying
(2x + 3)(x + -4) = 13

Reorder the terms:
(3 + 2x)(x + -4) = 13

Reorder the terms:
(3 + 2x)(-4 + x) = 13

Multiply (3 + 2x) * (-4 + x)
(3(-4 + x) + 2x * (-4 + x)) = 13
((-4 * 3 + x * 3) + 2x * (-4 + x)) = 13
((-12 + 3x) + 2x * (-4 + x)) = 13
(-12 + 3x + (-4 * 2x + x * 2x)) = 13
(-12 + 3x + (-8x + 2x2)) = 13

Combine like terms: 3x + -8x = -5x
(-12 + -5x + 2x2) = 13

Solving
-12 + -5x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
-12 + -13 + -5x + 2x2 = 13 + -13

Combine like terms: -12 + -13 = -25
-25 + -5x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-25 + -5x + 2x2 = 0

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


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 5}

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