(6x^2-7x+6)+(-8x^2-6)=0

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Solution for (6x^2-7x+6)+(-8x^2-6)=0 equation:


Simplifying
(6x2 + -7x + 6) + (-8x2 + -6) = 0

Reorder the terms:
(6 + -7x + 6x2) + (-8x2 + -6) = 0

Remove parenthesis around (6 + -7x + 6x2)
6 + -7x + 6x2 + (-8x2 + -6) = 0

Reorder the terms:
6 + -7x + 6x2 + (-6 + -8x2) = 0

Remove parenthesis around (-6 + -8x2)
6 + -7x + 6x2 + -6 + -8x2 = 0

Reorder the terms:
6 + -6 + -7x + 6x2 + -8x2 = 0

Combine like terms: 6 + -6 = 0
0 + -7x + 6x2 + -8x2 = 0
-7x + 6x2 + -8x2 = 0

Combine like terms: 6x2 + -8x2 = -2x2
-7x + -2x2 = 0

Solving
-7x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(7 + 2x) = 0

Ignore the factor -1.

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 '(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, -3.5}

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