(6x^2+2x-9)+(8x^2-5x+1)-(3x-4)(7x+2)=0

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Solution for (6x^2+2x-9)+(8x^2-5x+1)-(3x-4)(7x+2)=0 equation: 


Simplifying
(6x2 + 2x + -9) + (8x2 + -5x + 1) + -1(3x + -4)(7x + 2) = 0

Reorder the terms:
(-9 + 2x + 6x2) + (8x2 + -5x + 1) + -1(3x + -4)(7x + 2) = 0

Remove parenthesis around (-9 + 2x + 6x2)
-9 + 2x + 6x2 + (8x2 + -5x + 1) + -1(3x + -4)(7x + 2) = 0

Reorder the terms:
-9 + 2x + 6x2 + (1 + -5x + 8x2) + -1(3x + -4)(7x + 2) = 0

Remove parenthesis around (1 + -5x + 8x2)
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1(3x + -4)(7x + 2) = 0

Reorder the terms:
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1(-4 + 3x)(7x + 2) = 0

Reorder the terms:
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1(-4 + 3x)(2 + 7x) = 0

Multiply (-4 + 3x) * (2 + 7x)
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1(-4(2 + 7x) + 3x * (2 + 7x)) = 0
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1((2 * -4 + 7x * -4) + 3x * (2 + 7x)) = 0
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1((-8 + -28x) + 3x * (2 + 7x)) = 0
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1(-8 + -28x + (2 * 3x + 7x * 3x)) = 0
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1(-8 + -28x + (6x + 21x2)) = 0

Combine like terms: -28x + 6x = -22x
-9 + 2x + 6x2 + 1 + -5x + 8x2 + -1(-8 + -22x + 21x2) = 0
-9 + 2x + 6x2 + 1 + -5x + 8x2 + (-8 * -1 + -22x * -1 + 21x2 * -1) = 0
-9 + 2x + 6x2 + 1 + -5x + 8x2 + (8 + 22x + -21x2) = 0

Reorder the terms:
-9 + 1 + 8 + 2x + -5x + 22x + 6x2 + 8x2 + -21x2 = 0

Combine like terms: -9 + 1 = -8
-8 + 8 + 2x + -5x + 22x + 6x2 + 8x2 + -21x2 = 0

Combine like terms: -8 + 8 = 0
0 + 2x + -5x + 22x + 6x2 + 8x2 + -21x2 = 0
2x + -5x + 22x + 6x2 + 8x2 + -21x2 = 0

Combine like terms: 2x + -5x = -3x
-3x + 22x + 6x2 + 8x2 + -21x2 = 0

Combine like terms: -3x + 22x = 19x
19x + 6x2 + 8x2 + -21x2 = 0

Combine like terms: 6x2 + 8x2 = 14x2
19x + 14x2 + -21x2 = 0

Combine like terms: 14x2 + -21x2 = -7x2
19x + -7x2 = 0

Solving
19x + -7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(19 + -7x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(19 + -7x)' equal to zero and attempt to solve:

Simplifying
19 + -7x = 0

Solving
19 + -7x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -7x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -7x = 0 + -19
-7x = 0 + -19

Combine like terms: 0 + -19 = -19
-7x = -19

Divide each side by '-7'.
x = 2.714285714

Simplifying
x = 2.714285714
Solution
x = {0, 2.714285714}

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