6x(x-3)-(2x+7)(x-3)=0

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Solution for 6x(x-3)-(2x+7)(x-3)=0 equation: 


Simplifying
6x(x + -3) + -1(2x + 7)(x + -3) = 0

Reorder the terms:
6x(-3 + x) + -1(2x + 7)(x + -3) = 0
(-3 * 6x + x * 6x) + -1(2x + 7)(x + -3) = 0
(-18x + 6x2) + -1(2x + 7)(x + -3) = 0

Reorder the terms:
-18x + 6x2 + -1(7 + 2x)(x + -3) = 0

Reorder the terms:
-18x + 6x2 + -1(7 + 2x)(-3 + x) = 0

Multiply (7 + 2x) * (-3 + x)
-18x + 6x2 + -1(7(-3 + x) + 2x * (-3 + x)) = 0
-18x + 6x2 + -1((-3 * 7 + x * 7) + 2x * (-3 + x)) = 0
-18x + 6x2 + -1((-21 + 7x) + 2x * (-3 + x)) = 0
-18x + 6x2 + -1(-21 + 7x + (-3 * 2x + x * 2x)) = 0
-18x + 6x2 + -1(-21 + 7x + (-6x + 2x2)) = 0

Combine like terms: 7x + -6x = 1x
-18x + 6x2 + -1(-21 + 1x + 2x2) = 0
-18x + 6x2 + (-21 * -1 + 1x * -1 + 2x2 * -1) = 0
-18x + 6x2 + (21 + -1x + -2x2) = 0

Reorder the terms:
21 + -18x + -1x + 6x2 + -2x2 = 0

Combine like terms: -18x + -1x = -19x
21 + -19x + 6x2 + -2x2 = 0

Combine like terms: 6x2 + -2x2 = 4x2
21 + -19x + 4x2 = 0

Solving
21 + -19x + 4x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75

Subproblem 2
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
Solution
x = {1.75, 3}

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