(4x+7)(x-6)=12x+21

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Solution for (4x+7)(x-6)=12x+21 equation: 


Simplifying
(4x + 7)(x + -6) = 12x + 21

Reorder the terms:
(7 + 4x)(x + -6) = 12x + 21

Reorder the terms:
(7 + 4x)(-6 + x) = 12x + 21

Multiply (7 + 4x) * (-6 + x)
(7(-6 + x) + 4x * (-6 + x)) = 12x + 21
((-6 * 7 + x * 7) + 4x * (-6 + x)) = 12x + 21
((-42 + 7x) + 4x * (-6 + x)) = 12x + 21
(-42 + 7x + (-6 * 4x + x * 4x)) = 12x + 21
(-42 + 7x + (-24x + 4x2)) = 12x + 21

Combine like terms: 7x + -24x = -17x
(-42 + -17x + 4x2) = 12x + 21

Reorder the terms:
-42 + -17x + 4x2 = 21 + 12x

Solving
-42 + -17x + 4x2 = 21 + 12x

Solving for variable 'x'.

Reorder the terms:
-42 + -21 + -17x + -12x + 4x2 = 21 + 12x + -21 + -12x

Combine like terms: -42 + -21 = -63
-63 + -17x + -12x + 4x2 = 21 + 12x + -21 + -12x

Combine like terms: -17x + -12x = -29x
-63 + -29x + 4x2 = 21 + 12x + -21 + -12x

Reorder the terms:
-63 + -29x + 4x2 = 21 + -21 + 12x + -12x

Combine like terms: 21 + -21 = 0
-63 + -29x + 4x2 = 0 + 12x + -12x
-63 + -29x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-63 + -29x + 4x2 = 0

Factor a trinomial.
(-7 + -4x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1.75, 9}

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