(12x+3)(2x-7)-5x(2x-7)=

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Solution for (12x+3)(2x-7)-5x(2x-7)= equation: 


Simplifying
(12x + 3)(2x + -7) + -5x(2x + -7) = 0

Reorder the terms:
(3 + 12x)(2x + -7) + -5x(2x + -7) = 0

Reorder the terms:
(3 + 12x)(-7 + 2x) + -5x(2x + -7) = 0

Multiply (3 + 12x) * (-7 + 2x)
(3(-7 + 2x) + 12x * (-7 + 2x)) + -5x(2x + -7) = 0
((-7 * 3 + 2x * 3) + 12x * (-7 + 2x)) + -5x(2x + -7) = 0
((-21 + 6x) + 12x * (-7 + 2x)) + -5x(2x + -7) = 0
(-21 + 6x + (-7 * 12x + 2x * 12x)) + -5x(2x + -7) = 0
(-21 + 6x + (-84x + 24x2)) + -5x(2x + -7) = 0

Combine like terms: 6x + -84x = -78x
(-21 + -78x + 24x2) + -5x(2x + -7) = 0

Reorder the terms:
-21 + -78x + 24x2 + -5x(-7 + 2x) = 0
-21 + -78x + 24x2 + (-7 * -5x + 2x * -5x) = 0
-21 + -78x + 24x2 + (35x + -10x2) = 0

Reorder the terms:
-21 + -78x + 35x + 24x2 + -10x2 = 0

Combine like terms: -78x + 35x = -43x
-21 + -43x + 24x2 + -10x2 = 0

Combine like terms: 24x2 + -10x2 = 14x2
-21 + -43x + 14x2 = 0

Solving
-21 + -43x + 14x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-3 + -7x)' equal to zero and attempt to solve:

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 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 + -7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7x = 0 + 3
-7x = 0 + 3

Combine like terms: 0 + 3 = 3
-7x = 3

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-0.4285714286, 3.5}

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