(4x-5)(2x+3)=13

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Solution for (4x-5)(2x+3)=13 equation: 


Simplifying
(4x + -5)(2x + 3) = 13

Reorder the terms:
(-5 + 4x)(2x + 3) = 13

Reorder the terms:
(-5 + 4x)(3 + 2x) = 13

Multiply (-5 + 4x) * (3 + 2x)
(-5(3 + 2x) + 4x * (3 + 2x)) = 13
((3 * -5 + 2x * -5) + 4x * (3 + 2x)) = 13
((-15 + -10x) + 4x * (3 + 2x)) = 13
(-15 + -10x + (3 * 4x + 2x * 4x)) = 13
(-15 + -10x + (12x + 8x2)) = 13

Combine like terms: -10x + 12x = 2x
(-15 + 2x + 8x2) = 13

Solving
-15 + 2x + 8x2 = 13

Solving for variable 'x'.

Reorder the terms:
-15 + -13 + 2x + 8x2 = 13 + -13

Combine like terms: -15 + -13 = -28
-28 + 2x + 8x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-28 + 2x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + x + 4x2) = 0

Factor a trinomial.
2((-2 + -1x)(7 + -4x)) = 0

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-2, 1.75}

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