-10x^2-12x+45=-9x^2+1-5x

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Solution for -10x^2-12x+45=-9x^2+1-5x equation:


Simplifying
-10x2 + -12x + 45 = -9x2 + 1 + -5x

Reorder the terms:
45 + -12x + -10x2 = -9x2 + 1 + -5x

Reorder the terms:
45 + -12x + -10x2 = 1 + -5x + -9x2

Solving
45 + -12x + -10x2 = 1 + -5x + -9x2

Solving for variable 'x'.

Reorder the terms:
45 + -1 + -12x + 5x + -10x2 + 9x2 = 1 + -5x + -9x2 + -1 + 5x + 9x2

Combine like terms: 45 + -1 = 44
44 + -12x + 5x + -10x2 + 9x2 = 1 + -5x + -9x2 + -1 + 5x + 9x2

Combine like terms: -12x + 5x = -7x
44 + -7x + -10x2 + 9x2 = 1 + -5x + -9x2 + -1 + 5x + 9x2

Combine like terms: -10x2 + 9x2 = -1x2
44 + -7x + -1x2 = 1 + -5x + -9x2 + -1 + 5x + 9x2

Reorder the terms:
44 + -7x + -1x2 = 1 + -1 + -5x + 5x + -9x2 + 9x2

Combine like terms: 1 + -1 = 0
44 + -7x + -1x2 = 0 + -5x + 5x + -9x2 + 9x2
44 + -7x + -1x2 = -5x + 5x + -9x2 + 9x2

Combine like terms: -5x + 5x = 0
44 + -7x + -1x2 = 0 + -9x2 + 9x2
44 + -7x + -1x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
44 + -7x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(11 + x) = 0

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Simplifying x = -11

Solution

x = {4, -11}

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