(4x+5)(12x-1)=-2(x-64)

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Solution for (4x+5)(12x-1)=-2(x-64) equation: 


Simplifying
(4x + 5)(12x + -1) = -2(x + -64)

Reorder the terms:
(5 + 4x)(12x + -1) = -2(x + -64)

Reorder the terms:
(5 + 4x)(-1 + 12x) = -2(x + -64)

Multiply (5 + 4x) * (-1 + 12x)
(5(-1 + 12x) + 4x * (-1 + 12x)) = -2(x + -64)
((-1 * 5 + 12x * 5) + 4x * (-1 + 12x)) = -2(x + -64)
((-5 + 60x) + 4x * (-1 + 12x)) = -2(x + -64)
(-5 + 60x + (-1 * 4x + 12x * 4x)) = -2(x + -64)
(-5 + 60x + (-4x + 48x2)) = -2(x + -64)

Combine like terms: 60x + -4x = 56x
(-5 + 56x + 48x2) = -2(x + -64)

Reorder the terms:
-5 + 56x + 48x2 = -2(-64 + x)
-5 + 56x + 48x2 = (-64 * -2 + x * -2)
-5 + 56x + 48x2 = (128 + -2x)

Solving
-5 + 56x + 48x2 = 128 + -2x

Solving for variable 'x'.

Reorder the terms:
-5 + -128 + 56x + 2x + 48x2 = 128 + -2x + -128 + 2x

Combine like terms: -5 + -128 = -133
-133 + 56x + 2x + 48x2 = 128 + -2x + -128 + 2x

Combine like terms: 56x + 2x = 58x
-133 + 58x + 48x2 = 128 + -2x + -128 + 2x

Reorder the terms:
-133 + 58x + 48x2 = 128 + -128 + -2x + 2x

Combine like terms: 128 + -128 = 0
-133 + 58x + 48x2 = 0 + -2x + 2x
-133 + 58x + 48x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-133 + 58x + 48x2 = 0

Factor a trinomial.
(-19 + -8x)(7 + -6x) = 0


Subproblem 1
Set the factor '(-19 + -8x)' equal to zero and attempt to solve:

Simplifying
-19 + -8x = 0

Solving
-19 + -8x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -8x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -8x = 0 + 19
-8x = 0 + 19

Combine like terms: 0 + 19 = 19
-8x = 19

Divide each side by '-8'.
x = -2.375

Simplifying
x = -2.375

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-2.375, 1.166666667}

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