4x^2+12x+9-(9x^2+42x+49)=0

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Solution for 4x^2+12x+9-(9x^2+42x+49)=0 equation:


Simplifying
4x2 + 12x + 9 + -1(9x2 + 42x + 49) = 0

Reorder the terms:
4x2 + 12x + 9 + -1(49 + 42x + 9x2) = 0
4x2 + 12x + 9 + (49 * -1 + 42x * -1 + 9x2 * -1) = 0
4x2 + 12x + 9 + (-49 + -42x + -9x2) = 0

Reorder the terms:
9 + -49 + 12x + -42x + 4x2 + -9x2 = 0

Combine like terms: 9 + -49 = -40
-40 + 12x + -42x + 4x2 + -9x2 = 0

Combine like terms: 12x + -42x = -30x
-40 + -30x + 4x2 + -9x2 = 0

Combine like terms: 4x2 + -9x2 = -5x2
-40 + -30x + -5x2 = 0

Solving
-40 + -30x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-5'.
-5(8 + 6x + x2) = 0

Factor a trinomial.
-5((4 + x)(2 + x)) = 0

Ignore the factor -5.

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {-4, -2}

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