(-4x+7)(3x-3)=-66

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Solution for (-4x+7)(3x-3)=-66 equation: 


Simplifying
(-4x + 7)(3x + -3) = -66

Reorder the terms:
(7 + -4x)(3x + -3) = -66

Reorder the terms:
(7 + -4x)(-3 + 3x) = -66

Multiply (7 + -4x) * (-3 + 3x)
(7(-3 + 3x) + -4x * (-3 + 3x)) = -66
((-3 * 7 + 3x * 7) + -4x * (-3 + 3x)) = -66
((-21 + 21x) + -4x * (-3 + 3x)) = -66
(-21 + 21x + (-3 * -4x + 3x * -4x)) = -66
(-21 + 21x + (12x + -12x2)) = -66

Combine like terms: 21x + 12x = 33x
(-21 + 33x + -12x2) = -66

Solving
-21 + 33x + -12x2 = -66

Solving for variable 'x'.

Reorder the terms:
-21 + 66 + 33x + -12x2 = -66 + 66

Combine like terms: -21 + 66 = 45
45 + 33x + -12x2 = -66 + 66

Combine like terms: -66 + 66 = 0
45 + 33x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 11x + -4x2) = 0

Factor a trinomial.
3((15 + -4x)(1 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(15 + -4x)' equal to zero and attempt to solve:

Simplifying
15 + -4x = 0

Solving
15 + -4x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -4x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4x = 0 + -15
-4x = 0 + -15

Combine like terms: 0 + -15 = -15
-4x = -15

Divide each side by '-4'.
x = 3.75

Simplifying
x = 3.75

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {3.75, -1}

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