2(x-3)(x-3)+7=25

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Solution for 2(x-3)(x-3)+7=25 equation: 


Simplifying
2(x + -3)(x + -3) + 7 = 25

Reorder the terms:
2(-3 + x)(x + -3) + 7 = 25

Reorder the terms:
2(-3 + x)(-3 + x) + 7 = 25

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) + 7 = 25
2((-3 * -3 + x * -3) + x(-3 + x)) + 7 = 25
2((9 + -3x) + x(-3 + x)) + 7 = 25
2(9 + -3x + (-3 * x + x * x)) + 7 = 25
2(9 + -3x + (-3x + x2)) + 7 = 25

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) + 7 = 25
(9 * 2 + -6x * 2 + x2 * 2) + 7 = 25
(18 + -12x + 2x2) + 7 = 25

Reorder the terms:
18 + 7 + -12x + 2x2 = 25

Combine like terms: 18 + 7 = 25
25 + -12x + 2x2 = 25

Add '-25' to each side of the equation.
25 + -12x + -25 + 2x2 = 25 + -25

Reorder the terms:
25 + -25 + -12x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
0 + -12x + 2x2 = 25 + -25
-12x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-12x + 2x2 = 0

Solving
-12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6 + x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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
Solution
x = {0, 6}

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