(x-2)(7-3x)-(4-x)(7-3x)=-42

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Solution for (x-2)(7-3x)-(4-x)(7-3x)=-42 equation: 


Simplifying
(x + -2)(7 + -3x) + -1(4 + -1x)(7 + -3x) = -42

Reorder the terms:
(-2 + x)(7 + -3x) + -1(4 + -1x)(7 + -3x) = -42

Multiply (-2 + x) * (7 + -3x)
(-2(7 + -3x) + x(7 + -3x)) + -1(4 + -1x)(7 + -3x) = -42
((7 * -2 + -3x * -2) + x(7 + -3x)) + -1(4 + -1x)(7 + -3x) = -42
((-14 + 6x) + x(7 + -3x)) + -1(4 + -1x)(7 + -3x) = -42
(-14 + 6x + (7 * x + -3x * x)) + -1(4 + -1x)(7 + -3x) = -42
(-14 + 6x + (7x + -3x2)) + -1(4 + -1x)(7 + -3x) = -42

Combine like terms: 6x + 7x = 13x
(-14 + 13x + -3x2) + -1(4 + -1x)(7 + -3x) = -42

Multiply (4 + -1x) * (7 + -3x)
-14 + 13x + -3x2 + -1(4(7 + -3x) + -1x * (7 + -3x)) = -42
-14 + 13x + -3x2 + -1((7 * 4 + -3x * 4) + -1x * (7 + -3x)) = -42
-14 + 13x + -3x2 + -1((28 + -12x) + -1x * (7 + -3x)) = -42
-14 + 13x + -3x2 + -1(28 + -12x + (7 * -1x + -3x * -1x)) = -42
-14 + 13x + -3x2 + -1(28 + -12x + (-7x + 3x2)) = -42

Combine like terms: -12x + -7x = -19x
-14 + 13x + -3x2 + -1(28 + -19x + 3x2) = -42
-14 + 13x + -3x2 + (28 * -1 + -19x * -1 + 3x2 * -1) = -42
-14 + 13x + -3x2 + (-28 + 19x + -3x2) = -42

Reorder the terms:
-14 + -28 + 13x + 19x + -3x2 + -3x2 = -42

Combine like terms: -14 + -28 = -42
-42 + 13x + 19x + -3x2 + -3x2 = -42

Combine like terms: 13x + 19x = 32x
-42 + 32x + -3x2 + -3x2 = -42

Combine like terms: -3x2 + -3x2 = -6x2
-42 + 32x + -6x2 = -42

Add '42' to each side of the equation.
-42 + 32x + 42 + -6x2 = -42 + 42

Reorder the terms:
-42 + 42 + 32x + -6x2 = -42 + 42

Combine like terms: -42 + 42 = 0
0 + 32x + -6x2 = -42 + 42
32x + -6x2 = -42 + 42

Combine like terms: -42 + 42 = 0
32x + -6x2 = 0

Solving
32x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(16 + -3x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 5.333333333}

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