4(x+5)-0.5(x-3)(6-2x)=x^2+1

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Solution for 4(x+5)-0.5(x-3)(6-2x)=x^2+1 equation:


Simplifying
4(x + 5) + -0.5(x + -3)(6 + -2x) = x2 + 1

Reorder the terms:
4(5 + x) + -0.5(x + -3)(6 + -2x) = x2 + 1
(5 * 4 + x * 4) + -0.5(x + -3)(6 + -2x) = x2 + 1
(20 + 4x) + -0.5(x + -3)(6 + -2x) = x2 + 1

Reorder the terms:
20 + 4x + -0.5(-3 + x)(6 + -2x) = x2 + 1

Multiply (-3 + x) * (6 + -2x)
20 + 4x + -0.5(-3(6 + -2x) + x(6 + -2x)) = x2 + 1
20 + 4x + -0.5((6 * -3 + -2x * -3) + x(6 + -2x)) = x2 + 1
20 + 4x + -0.5((-18 + 6x) + x(6 + -2x)) = x2 + 1
20 + 4x + -0.5(-18 + 6x + (6 * x + -2x * x)) = x2 + 1
20 + 4x + -0.5(-18 + 6x + (6x + -2x2)) = x2 + 1

Combine like terms: 6x + 6x = 12x
20 + 4x + -0.5(-18 + 12x + -2x2) = x2 + 1
20 + 4x + (-18 * -0.5 + 12x * -0.5 + -2x2 * -0.5) = x2 + 1
20 + 4x + (9 + -6x + 1x2) = x2 + 1

Reorder the terms:
20 + 9 + 4x + -6x + 1x2 = x2 + 1

Combine like terms: 20 + 9 = 29
29 + 4x + -6x + 1x2 = x2 + 1

Combine like terms: 4x + -6x = -2x
29 + -2x + 1x2 = x2 + 1

Reorder the terms:
29 + -2x + 1x2 = 1 + x2

Solving
29 + -2x + 1x2 = 1 + x2

Solving for variable 'x'.

Reorder the terms:
29 + -1 + -2x + 1x2 + -1x2 = 1 + x2 + -1 + -1x2

Combine like terms: 29 + -1 = 28
28 + -2x + 1x2 + -1x2 = 1 + x2 + -1 + -1x2

Combine like terms: 1x2 + -1x2 = 0
28 + -2x + 0 = 1 + x2 + -1 + -1x2
28 + -2x = 1 + x2 + -1 + -1x2

Reorder the terms:
28 + -2x = 1 + -1 + x2 + -1x2

Combine like terms: 1 + -1 = 0
28 + -2x = 0 + x2 + -1x2
28 + -2x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + -2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {14}

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