(4x-3)(5x-4)=12

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Solution for (4x-3)(5x-4)=12 equation: 


Simplifying
(4x + -3)(5x + -4) = 12

Reorder the terms:
(-3 + 4x)(5x + -4) = 12

Reorder the terms:
(-3 + 4x)(-4 + 5x) = 12

Multiply (-3 + 4x) * (-4 + 5x)
(-3(-4 + 5x) + 4x * (-4 + 5x)) = 12
((-4 * -3 + 5x * -3) + 4x * (-4 + 5x)) = 12
((12 + -15x) + 4x * (-4 + 5x)) = 12
(12 + -15x + (-4 * 4x + 5x * 4x)) = 12
(12 + -15x + (-16x + 20x2)) = 12

Combine like terms: -15x + -16x = -31x
(12 + -31x + 20x2) = 12

Add '-12' to each side of the equation.
12 + -31x + -12 + 20x2 = 12 + -12

Reorder the terms:
12 + -12 + -31x + 20x2 = 12 + -12

Combine like terms: 12 + -12 = 0
0 + -31x + 20x2 = 12 + -12
-31x + 20x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-31x + 20x2 = 0

Solving
-31x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-31 + 20x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-31 + 20x)' equal to zero and attempt to solve:

Simplifying
-31 + 20x = 0

Solving
-31 + 20x = 0

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

Add '31' to each side of the equation.
-31 + 31 + 20x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 20x = 0 + 31
20x = 0 + 31

Combine like terms: 0 + 31 = 31
20x = 31

Divide each side by '20'.
x = 1.55

Simplifying
x = 1.55
Solution
x = {0, 1.55}

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