=40x^2-66x+20

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Solution for =40x^2-66x+20 equation:


Simplifying
0 = 40x2 + -66x + 20

Reorder the terms:
0 = 20 + -66x + 40x2

Solving
0 = 20 + -66x + 40x2

Solving for variable 'x'.

Combine like terms: 0 + -20 = -20
-20 + 66x + -40x2 = 20 + -66x + 40x2 + -20 + 66x + -40x2

Reorder the terms:
-20 + 66x + -40x2 = 20 + -20 + -66x + 66x + 40x2 + -40x2

Combine like terms: 20 + -20 = 0
-20 + 66x + -40x2 = 0 + -66x + 66x + 40x2 + -40x2
-20 + 66x + -40x2 = -66x + 66x + 40x2 + -40x2

Combine like terms: -66x + 66x = 0
-20 + 66x + -40x2 = 0 + 40x2 + -40x2
-20 + 66x + -40x2 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
-20 + 66x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 33x + -20x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 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 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Divide each side by '4'. x = 1.25 Simplifying x = 1.25

Subproblem 2

Set the factor '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4

Solution

x = {1.25, 0.4}

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