10x^2+30x+40x=180

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Solution for 10x^2+30x+40x=180 equation:


Simplifying
10x2 + 30x + 40x = 180

Reorder the terms:
30x + 40x + 10x2 = 180

Combine like terms: 30x + 40x = 70x
70x + 10x2 = 180

Solving
70x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 70x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 70x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-18 + 7x + x2) = 0

Factor a trinomial.
10((-9 + -1x)(2 + -1x)) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-9, 2}

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