21(x-4)=(2x-7)(x+2)

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Solution for 21(x-4)=(2x-7)(x+2) equation: 


Simplifying
21(x + -4) = (2x + -7)(x + 2)

Reorder the terms:
21(-4 + x) = (2x + -7)(x + 2)
(-4 * 21 + x * 21) = (2x + -7)(x + 2)
(-84 + 21x) = (2x + -7)(x + 2)

Reorder the terms:
-84 + 21x = (-7 + 2x)(x + 2)

Reorder the terms:
-84 + 21x = (-7 + 2x)(2 + x)

Multiply (-7 + 2x) * (2 + x)
-84 + 21x = (-7(2 + x) + 2x * (2 + x))
-84 + 21x = ((2 * -7 + x * -7) + 2x * (2 + x))
-84 + 21x = ((-14 + -7x) + 2x * (2 + x))
-84 + 21x = (-14 + -7x + (2 * 2x + x * 2x))
-84 + 21x = (-14 + -7x + (4x + 2x2))

Combine like terms: -7x + 4x = -3x
-84 + 21x = (-14 + -3x + 2x2)

Solving
-84 + 21x = -14 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-84 + 14 + 21x + 3x + -2x2 = -14 + -3x + 2x2 + 14 + 3x + -2x2

Combine like terms: -84 + 14 = -70
-70 + 21x + 3x + -2x2 = -14 + -3x + 2x2 + 14 + 3x + -2x2

Combine like terms: 21x + 3x = 24x
-70 + 24x + -2x2 = -14 + -3x + 2x2 + 14 + 3x + -2x2

Reorder the terms:
-70 + 24x + -2x2 = -14 + 14 + -3x + 3x + 2x2 + -2x2

Combine like terms: -14 + 14 = 0
-70 + 24x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2
-70 + 24x + -2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-70 + 24x + -2x2 = 0 + 2x2 + -2x2
-70 + 24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-70 + 24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 12x + -1x2) = 0

Factor a trinomial.
2((-7 + x)(5 + -1x)) = 0

Ignore the factor 2.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {7, 5}

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