=(x-7)(3x-2)

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Solution for =(x-7)(3x-2) equation: 


Simplifying
0 = (x + -7)(3x + -2)

Reorder the terms:
0 = (-7 + x)(3x + -2)

Reorder the terms:
0 = (-7 + x)(-2 + 3x)

Multiply (-7 + x) * (-2 + 3x)
0 = (-7(-2 + 3x) + x(-2 + 3x))
0 = ((-2 * -7 + 3x * -7) + x(-2 + 3x))
0 = ((14 + -21x) + x(-2 + 3x))
0 = (14 + -21x + (-2 * x + 3x * x))
0 = (14 + -21x + (-2x + 3x2))

Combine like terms: -21x + -2x = -23x
0 = (14 + -23x + 3x2)

Solving
0 = 14 + -23x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -14 = -14
-14 + 23x + -3x2 = 14 + -23x + 3x2 + -14 + 23x + -3x2

Reorder the terms:
-14 + 23x + -3x2 = 14 + -14 + -23x + 23x + 3x2 + -3x2

Combine like terms: 14 + -14 = 0
-14 + 23x + -3x2 = 0 + -23x + 23x + 3x2 + -3x2
-14 + 23x + -3x2 = -23x + 23x + 3x2 + -3x2

Combine like terms: -23x + 23x = 0
-14 + 23x + -3x2 = 0 + 3x2 + -3x2
-14 + 23x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-14 + 23x + -3x2 = 0

Factor a trinomial.
(-7 + x)(2 + -3x) = 0


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

Simplifying
-7 + x = 0

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

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

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

Simplifying
x = 7

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {7, 0.6666666667}

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