(2x-3)(4x-5)=105

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Solution for (2x-3)(4x-5)=105 equation:


Simplifying
(2x + -3)(4x + -5) = 105

Reorder the terms:
(-3 + 2x)(4x + -5) = 105

Reorder the terms:
(-3 + 2x)(-5 + 4x) = 105

Multiply (-3 + 2x) * (-5 + 4x)
(-3(-5 + 4x) + 2x * (-5 + 4x)) = 105
((-5 * -3 + 4x * -3) + 2x * (-5 + 4x)) = 105
((15 + -12x) + 2x * (-5 + 4x)) = 105
(15 + -12x + (-5 * 2x + 4x * 2x)) = 105
(15 + -12x + (-10x + 8x2)) = 105

Combine like terms: -12x + -10x = -22x
(15 + -22x + 8x2) = 105

Solving
15 + -22x + 8x2 = 105

Solving for variable 'x'.

Reorder the terms:
15 + -105 + -22x + 8x2 = 105 + -105

Combine like terms: 15 + -105 = -90
-90 + -22x + 8x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-90 + -22x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -11x + 4x2) = 0

Factor a trinomial.
2((-9 + -4x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

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 = {-2.25, 5}

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