(3x+6)(4x-3)=357

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Solution for (3x+6)(4x-3)=357 equation: 


Simplifying
(3x + 6)(4x + -3) = 357

Reorder the terms:
(6 + 3x)(4x + -3) = 357

Reorder the terms:
(6 + 3x)(-3 + 4x) = 357

Multiply (6 + 3x) * (-3 + 4x)
(6(-3 + 4x) + 3x * (-3 + 4x)) = 357
((-3 * 6 + 4x * 6) + 3x * (-3 + 4x)) = 357
((-18 + 24x) + 3x * (-3 + 4x)) = 357
(-18 + 24x + (-3 * 3x + 4x * 3x)) = 357
(-18 + 24x + (-9x + 12x2)) = 357

Combine like terms: 24x + -9x = 15x
(-18 + 15x + 12x2) = 357

Solving
-18 + 15x + 12x2 = 357

Solving for variable 'x'.

Reorder the terms:
-18 + -357 + 15x + 12x2 = 357 + -357

Combine like terms: -18 + -357 = -375
-375 + 15x + 12x2 = 357 + -357

Combine like terms: 357 + -357 = 0
-375 + 15x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-125 + 5x + 4x2) = 0

Factor a trinomial.
3((-25 + -4x)(5 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-25 + -4x)' equal to zero and attempt to solve:

Simplifying
-25 + -4x = 0

Solving
-25 + -4x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -4x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -4x = 0 + 25
-4x = 0 + 25

Combine like terms: 0 + 25 = 25
-4x = 25

Divide each side by '-4'.
x = -6.25

Simplifying
x = -6.25

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 = {-6.25, 5}

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