625=x^2+4x^2-40x+100

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Solution for 625=x^2+4x^2-40x+100 equation: 


Simplifying
625 = x2 + 4x2 + -40x + 100

Reorder the terms:
625 = 100 + -40x + x2 + 4x2

Combine like terms: x2 + 4x2 = 5x2
625 = 100 + -40x + 5x2

Solving
625 = 100 + -40x + 5x2

Solving for variable 'x'.

Combine like terms: 625 + -100 = 525
525 + 40x + -5x2 = 100 + -40x + 5x2 + -100 + 40x + -5x2

Reorder the terms:
525 + 40x + -5x2 = 100 + -100 + -40x + 40x + 5x2 + -5x2

Combine like terms: 100 + -100 = 0
525 + 40x + -5x2 = 0 + -40x + 40x + 5x2 + -5x2
525 + 40x + -5x2 = -40x + 40x + 5x2 + -5x2

Combine like terms: -40x + 40x = 0
525 + 40x + -5x2 = 0 + 5x2 + -5x2
525 + 40x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
525 + 40x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(105 + 8x + -1x2) = 0

Factor a trinomial.
5((15 + -1x)(7 + x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {15, -7}

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