(x-5)(2x-14)=4(3x-21)

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Solution for (x-5)(2x-14)=4(3x-21) equation: 


Simplifying
(x + -5)(2x + -14) = 4(3x + -21)

Reorder the terms:
(-5 + x)(2x + -14) = 4(3x + -21)

Reorder the terms:
(-5 + x)(-14 + 2x) = 4(3x + -21)

Multiply (-5 + x) * (-14 + 2x)
(-5(-14 + 2x) + x(-14 + 2x)) = 4(3x + -21)
((-14 * -5 + 2x * -5) + x(-14 + 2x)) = 4(3x + -21)
((70 + -10x) + x(-14 + 2x)) = 4(3x + -21)
(70 + -10x + (-14 * x + 2x * x)) = 4(3x + -21)
(70 + -10x + (-14x + 2x2)) = 4(3x + -21)

Combine like terms: -10x + -14x = -24x
(70 + -24x + 2x2) = 4(3x + -21)

Reorder the terms:
70 + -24x + 2x2 = 4(-21 + 3x)
70 + -24x + 2x2 = (-21 * 4 + 3x * 4)
70 + -24x + 2x2 = (-84 + 12x)

Solving
70 + -24x + 2x2 = -84 + 12x

Solving for variable 'x'.

Reorder the terms:
70 + 84 + -24x + -12x + 2x2 = -84 + 12x + 84 + -12x

Combine like terms: 70 + 84 = 154
154 + -24x + -12x + 2x2 = -84 + 12x + 84 + -12x

Combine like terms: -24x + -12x = -36x
154 + -36x + 2x2 = -84 + 12x + 84 + -12x

Reorder the terms:
154 + -36x + 2x2 = -84 + 84 + 12x + -12x

Combine like terms: -84 + 84 = 0
154 + -36x + 2x2 = 0 + 12x + -12x
154 + -36x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
154 + -36x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(77 + -18x + x2) = 0

Factor a trinomial.
2((7 + -1x)(11 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {7, 11}

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