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

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


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

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

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

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

Combine like terms: 8x + -3x = 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 + -1x)(5 + -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 '(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
Solution
x = {-5, 2.5}

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