(3x+6)(4x-7)=

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Solution for (3x+6)(4x-7)= equation: 


Simplifying
(3x + 6)(4x + -7) = 0

Reorder the terms:
(6 + 3x)(4x + -7) = 0

Reorder the terms:
(6 + 3x)(-7 + 4x) = 0

Multiply (6 + 3x) * (-7 + 4x)
(6(-7 + 4x) + 3x * (-7 + 4x)) = 0
((-7 * 6 + 4x * 6) + 3x * (-7 + 4x)) = 0
((-42 + 24x) + 3x * (-7 + 4x)) = 0
(-42 + 24x + (-7 * 3x + 4x * 3x)) = 0
(-42 + 24x + (-21x + 12x2)) = 0

Combine like terms: 24x + -21x = 3x
(-42 + 3x + 12x2) = 0

Solving
-42 + 3x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + x + 4x2) = 0

Factor a trinomial.
3((-2 + -1x)(7 + -4x)) = 0

Ignore the factor 3.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
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
Solution
x = {-2, 1.75}

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