(11x^2+48)-(x-8)(x-6)=0

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Solution for (11x^2+48)-(x-8)(x-6)=0 equation: 


Simplifying
(11x2 + 48) + -1(x + -8)(x + -6) = 0

Reorder the terms:
(48 + 11x2) + -1(x + -8)(x + -6) = 0

Remove parenthesis around (48 + 11x2)
48 + 11x2 + -1(x + -8)(x + -6) = 0

Reorder the terms:
48 + 11x2 + -1(-8 + x)(x + -6) = 0

Reorder the terms:
48 + 11x2 + -1(-8 + x)(-6 + x) = 0

Multiply (-8 + x) * (-6 + x)
48 + 11x2 + -1(-8(-6 + x) + x(-6 + x)) = 0
48 + 11x2 + -1((-6 * -8 + x * -8) + x(-6 + x)) = 0
48 + 11x2 + -1((48 + -8x) + x(-6 + x)) = 0
48 + 11x2 + -1(48 + -8x + (-6 * x + x * x)) = 0
48 + 11x2 + -1(48 + -8x + (-6x + x2)) = 0

Combine like terms: -8x + -6x = -14x
48 + 11x2 + -1(48 + -14x + x2) = 0
48 + 11x2 + (48 * -1 + -14x * -1 + x2 * -1) = 0
48 + 11x2 + (-48 + 14x + -1x2) = 0

Reorder the terms:
48 + -48 + 14x + 11x2 + -1x2 = 0

Combine like terms: 48 + -48 = 0
0 + 14x + 11x2 + -1x2 = 0
14x + 11x2 + -1x2 = 0

Combine like terms: 11x2 + -1x2 = 10x2
14x + 10x2 = 0

Solving
14x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7 + 5x) = 0

Ignore the factor 2.

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 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 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 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4
Solution
x = {0, -1.4}

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