26x^2+120x+150=8x^2

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Solution for 26x^2+120x+150=8x^2 equation:


Simplifying
26x2 + 120x + 150 = 8x2

Reorder the terms:
150 + 120x + 26x2 = 8x2

Solving
150 + 120x + 26x2 = 8x2

Solving for variable 'x'.

Combine like terms: 26x2 + -8x2 = 18x2
150 + 120x + 18x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
150 + 120x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(25 + 20x + 3x2) = 0

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

Ignore the factor 6.

Subproblem 1

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

Subproblem 2

Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667

Solution

x = {-5, -1.666666667}

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