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

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


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

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

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

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

Combine like terms: -16x + -15x = -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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