9(4x^2+4x+1)=4(x^2-10x+25)

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Solution for 9(4x^2+4x+1)=4(x^2-10x+25) equation: 


Simplifying
9(4x2 + 4x + 1) = 4(x2 + -10x + 25)

Reorder the terms:
9(1 + 4x + 4x2) = 4(x2 + -10x + 25)
(1 * 9 + 4x * 9 + 4x2 * 9) = 4(x2 + -10x + 25)
(9 + 36x + 36x2) = 4(x2 + -10x + 25)

Reorder the terms:
9 + 36x + 36x2 = 4(25 + -10x + x2)
9 + 36x + 36x2 = (25 * 4 + -10x * 4 + x2 * 4)
9 + 36x + 36x2 = (100 + -40x + 4x2)

Solving
9 + 36x + 36x2 = 100 + -40x + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + -100 + 36x + 40x + 36x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 9 + -100 = -91
-91 + 36x + 40x + 36x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 36x + 40x = 76x
-91 + 76x + 36x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 36x2 + -4x2 = 32x2
-91 + 76x + 32x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Reorder the terms:
-91 + 76x + 32x2 = 100 + -100 + -40x + 40x + 4x2 + -4x2

Combine like terms: 100 + -100 = 0
-91 + 76x + 32x2 = 0 + -40x + 40x + 4x2 + -4x2
-91 + 76x + 32x2 = -40x + 40x + 4x2 + -4x2

Combine like terms: -40x + 40x = 0
-91 + 76x + 32x2 = 0 + 4x2 + -4x2
-91 + 76x + 32x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-91 + 76x + 32x2 = 0

Factor a trinomial.
(-13 + -4x)(7 + -8x) = 0


Subproblem 1
Set the factor '(-13 + -4x)' equal to zero and attempt to solve:

Simplifying
-13 + -4x = 0

Solving
-13 + -4x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -4x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4x = 0 + 13
-4x = 0 + 13

Combine like terms: 0 + 13 = 13
-4x = 13

Divide each side by '-4'.
x = -3.25

Simplifying
x = -3.25

Subproblem 2
Set the factor '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 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 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875
Solution
x = {-3.25, 0.875}

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