7x^2+69x+218=4x^2+36x+128

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Solution for 7x^2+69x+218=4x^2+36x+128 equation:


Simplifying
7x2 + 69x + 218 = 4x2 + 36x + 128

Reorder the terms:
218 + 69x + 7x2 = 4x2 + 36x + 128

Reorder the terms:
218 + 69x + 7x2 = 128 + 36x + 4x2

Solving
218 + 69x + 7x2 = 128 + 36x + 4x2

Solving for variable 'x'.

Reorder the terms:
218 + -128 + 69x + -36x + 7x2 + -4x2 = 128 + 36x + 4x2 + -128 + -36x + -4x2

Combine like terms: 218 + -128 = 90
90 + 69x + -36x + 7x2 + -4x2 = 128 + 36x + 4x2 + -128 + -36x + -4x2

Combine like terms: 69x + -36x = 33x
90 + 33x + 7x2 + -4x2 = 128 + 36x + 4x2 + -128 + -36x + -4x2

Combine like terms: 7x2 + -4x2 = 3x2
90 + 33x + 3x2 = 128 + 36x + 4x2 + -128 + -36x + -4x2

Reorder the terms:
90 + 33x + 3x2 = 128 + -128 + 36x + -36x + 4x2 + -4x2

Combine like terms: 128 + -128 = 0
90 + 33x + 3x2 = 0 + 36x + -36x + 4x2 + -4x2
90 + 33x + 3x2 = 36x + -36x + 4x2 + -4x2

Combine like terms: 36x + -36x = 0
90 + 33x + 3x2 = 0 + 4x2 + -4x2
90 + 33x + 3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
90 + 33x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + 11x + x2) = 0

Factor a trinomial.
3((6 + x)(5 + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {-6, -5}

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