(-7x+16)(12x-3)=0

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Solution for (-7x+16)(12x-3)=0 equation: 


Simplifying
(-7x + 16)(12x + -3) = 0

Reorder the terms:
(16 + -7x)(12x + -3) = 0

Reorder the terms:
(16 + -7x)(-3 + 12x) = 0

Multiply (16 + -7x) * (-3 + 12x)
(16(-3 + 12x) + -7x * (-3 + 12x)) = 0
((-3 * 16 + 12x * 16) + -7x * (-3 + 12x)) = 0
((-48 + 192x) + -7x * (-3 + 12x)) = 0
(-48 + 192x + (-3 * -7x + 12x * -7x)) = 0
(-48 + 192x + (21x + -84x2)) = 0

Combine like terms: 192x + 21x = 213x
(-48 + 213x + -84x2) = 0

Solving
-48 + 213x + -84x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 71x + -28x2) = 0

Factor a trinomial.
3((-16 + 7x)(1 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-16 + 7x)' equal to zero and attempt to solve:

Simplifying
-16 + 7x = 0

Solving
-16 + 7x = 0

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

Add '16' to each side of the equation.
-16 + 16 + 7x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 7x = 0 + 16
7x = 0 + 16

Combine like terms: 0 + 16 = 16
7x = 16

Divide each side by '7'.
x = 2.285714286

Simplifying
x = 2.285714286

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {2.285714286, 0.25}

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