(7x-12)(2x+1)-(4x+6)(7x-12)=0

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Solution for (7x-12)(2x+1)-(4x+6)(7x-12)=0 equation: 


Simplifying
(7x + -12)(2x + 1) + -1(4x + 6)(7x + -12) = 0

Reorder the terms:
(-12 + 7x)(2x + 1) + -1(4x + 6)(7x + -12) = 0

Reorder the terms:
(-12 + 7x)(1 + 2x) + -1(4x + 6)(7x + -12) = 0

Multiply (-12 + 7x) * (1 + 2x)
(-12(1 + 2x) + 7x * (1 + 2x)) + -1(4x + 6)(7x + -12) = 0
((1 * -12 + 2x * -12) + 7x * (1 + 2x)) + -1(4x + 6)(7x + -12) = 0
((-12 + -24x) + 7x * (1 + 2x)) + -1(4x + 6)(7x + -12) = 0
(-12 + -24x + (1 * 7x + 2x * 7x)) + -1(4x + 6)(7x + -12) = 0
(-12 + -24x + (7x + 14x2)) + -1(4x + 6)(7x + -12) = 0

Combine like terms: -24x + 7x = -17x
(-12 + -17x + 14x2) + -1(4x + 6)(7x + -12) = 0

Reorder the terms:
-12 + -17x + 14x2 + -1(6 + 4x)(7x + -12) = 0

Reorder the terms:
-12 + -17x + 14x2 + -1(6 + 4x)(-12 + 7x) = 0

Multiply (6 + 4x) * (-12 + 7x)
-12 + -17x + 14x2 + -1(6(-12 + 7x) + 4x * (-12 + 7x)) = 0
-12 + -17x + 14x2 + -1((-12 * 6 + 7x * 6) + 4x * (-12 + 7x)) = 0
-12 + -17x + 14x2 + -1((-72 + 42x) + 4x * (-12 + 7x)) = 0
-12 + -17x + 14x2 + -1(-72 + 42x + (-12 * 4x + 7x * 4x)) = 0
-12 + -17x + 14x2 + -1(-72 + 42x + (-48x + 28x2)) = 0

Combine like terms: 42x + -48x = -6x
-12 + -17x + 14x2 + -1(-72 + -6x + 28x2) = 0
-12 + -17x + 14x2 + (-72 * -1 + -6x * -1 + 28x2 * -1) = 0
-12 + -17x + 14x2 + (72 + 6x + -28x2) = 0

Reorder the terms:
-12 + 72 + -17x + 6x + 14x2 + -28x2 = 0

Combine like terms: -12 + 72 = 60
60 + -17x + 6x + 14x2 + -28x2 = 0

Combine like terms: -17x + 6x = -11x
60 + -11x + 14x2 + -28x2 = 0

Combine like terms: 14x2 + -28x2 = -14x2
60 + -11x + -14x2 = 0

Solving
60 + -11x + -14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(12 + -7x)(5 + 2x) = 0


Subproblem 1
Set the factor '(12 + -7x)' equal to zero and attempt to solve:

Simplifying
12 + -7x = 0

Solving
12 + -7x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -7x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -7x = 0 + -12
-7x = 0 + -12

Combine like terms: 0 + -12 = -12
-7x = -12

Divide each side by '-7'.
x = 1.714285714

Simplifying
x = 1.714285714

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {1.714285714, -2.5}

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