49-x^2=(x+7)(2x-3)

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Solution for 49-x^2=(x+7)(2x-3) equation: 


Simplifying
49 + -1x2 = (x + 7)(2x + -3)

Reorder the terms:
49 + -1x2 = (7 + x)(2x + -3)

Reorder the terms:
49 + -1x2 = (7 + x)(-3 + 2x)

Multiply (7 + x) * (-3 + 2x)
49 + -1x2 = (7(-3 + 2x) + x(-3 + 2x))
49 + -1x2 = ((-3 * 7 + 2x * 7) + x(-3 + 2x))
49 + -1x2 = ((-21 + 14x) + x(-3 + 2x))
49 + -1x2 = (-21 + 14x + (-3 * x + 2x * x))
49 + -1x2 = (-21 + 14x + (-3x + 2x2))

Combine like terms: 14x + -3x = 11x
49 + -1x2 = (-21 + 11x + 2x2)

Solving
49 + -1x2 = -21 + 11x + 2x2

Solving for variable 'x'.

Reorder the terms:
49 + 21 + -11x + -1x2 + -2x2 = -21 + 11x + 2x2 + 21 + -11x + -2x2

Combine like terms: 49 + 21 = 70
70 + -11x + -1x2 + -2x2 = -21 + 11x + 2x2 + 21 + -11x + -2x2

Combine like terms: -1x2 + -2x2 = -3x2
70 + -11x + -3x2 = -21 + 11x + 2x2 + 21 + -11x + -2x2

Reorder the terms:
70 + -11x + -3x2 = -21 + 21 + 11x + -11x + 2x2 + -2x2

Combine like terms: -21 + 21 = 0
70 + -11x + -3x2 = 0 + 11x + -11x + 2x2 + -2x2
70 + -11x + -3x2 = 11x + -11x + 2x2 + -2x2

Combine like terms: 11x + -11x = 0
70 + -11x + -3x2 = 0 + 2x2 + -2x2
70 + -11x + -3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
70 + -11x + -3x2 = 0

Factor a trinomial.
(10 + -3x)(7 + x) = 0


Subproblem 1
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333

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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7
Solution
x = {3.333333333, -7}

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