(3x-4)(x-7)=-20

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Solution for (3x-4)(x-7)=-20 equation: 


Simplifying
(3x + -4)(x + -7) = -20

Reorder the terms:
(-4 + 3x)(x + -7) = -20

Reorder the terms:
(-4 + 3x)(-7 + x) = -20

Multiply (-4 + 3x) * (-7 + x)
(-4(-7 + x) + 3x * (-7 + x)) = -20
((-7 * -4 + x * -4) + 3x * (-7 + x)) = -20
((28 + -4x) + 3x * (-7 + x)) = -20
(28 + -4x + (-7 * 3x + x * 3x)) = -20
(28 + -4x + (-21x + 3x2)) = -20

Combine like terms: -4x + -21x = -25x
(28 + -25x + 3x2) = -20

Solving
28 + -25x + 3x2 = -20

Solving for variable 'x'.

Reorder the terms:
28 + 20 + -25x + 3x2 = -20 + 20

Combine like terms: 28 + 20 = 48
48 + -25x + 3x2 = -20 + 20

Combine like terms: -20 + 20 = 0
48 + -25x + 3x2 = 0

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


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(16 + -3x)' equal to zero and attempt to solve:

Simplifying
16 + -3x = 0

Solving
16 + -3x = 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 + -3x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3x = 0 + -16
-3x = 0 + -16

Combine like terms: 0 + -16 = -16
-3x = -16

Divide each side by '-3'.
x = 5.333333333

Simplifying
x = 5.333333333
Solution
x = {3, 5.333333333}

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