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

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


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

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

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

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

Combine like terms: 12x + -10x = 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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