(7x-27)(4x+12)=

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Solution for (7x-27)(4x+12)= equation: 


Simplifying
(7x + -27)(4x + 12) = 0

Reorder the terms:
(-27 + 7x)(4x + 12) = 0

Reorder the terms:
(-27 + 7x)(12 + 4x) = 0

Multiply (-27 + 7x) * (12 + 4x)
(-27(12 + 4x) + 7x * (12 + 4x)) = 0
((12 * -27 + 4x * -27) + 7x * (12 + 4x)) = 0
((-324 + -108x) + 7x * (12 + 4x)) = 0
(-324 + -108x + (12 * 7x + 4x * 7x)) = 0
(-324 + -108x + (84x + 28x2)) = 0

Combine like terms: -108x + 84x = -24x
(-324 + -24x + 28x2) = 0

Solving
-324 + -24x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-81 + -6x + 7x2) = 0

Factor a trinomial.
4((-3 + -1x)(27 + -7x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(27 + -7x)' equal to zero and attempt to solve:

Simplifying
27 + -7x = 0

Solving
27 + -7x = 0

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

Add '-27' to each side of the equation.
27 + -27 + -7x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -7x = 0 + -27
-7x = 0 + -27

Combine like terms: 0 + -27 = -27
-7x = -27

Divide each side by '-7'.
x = 3.857142857

Simplifying
x = 3.857142857
Solution
x = {-3, 3.857142857}

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